33:I[196793,["/_next/static/chunks/2msykuvi-vydm.js?dpl=nogit-1790362613","/_next/static/chunks/2mu6-wo6ccpi3.js?dpl=nogit-1790362613","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790362613","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790362613","/_next/static/chunks/0p4rexedanx97.js?dpl=nogit-1790362613","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790362613","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790362613","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790362613","/_next/static/chunks/3lf9kdvvybemj.js?dpl=nogit-1790362613","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790362613","/_next/static/chunks/03q735zs9dbpu.js?dpl=nogit-1790362613","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790362613","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790362613","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790362613","/_next/static/chunks/12xoy6h_w_le6.js?dpl=nogit-1790362613","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790362613","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790362613","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790362613","/_next/static/chunks/32qmkt01ta8b2.js?dpl=nogit-1790362613","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790362613","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790362613","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790362613","/_next/static/chunks/14kf-an-d2n-e.js?dpl=nogit-1790362613","/_next/static/chunks/381o-754ev9ia.js?dpl=nogit-1790362613","/_next/static/chunks/2tr2cll18vqv3.js?dpl=nogit-1790362613","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790362613","/_next/static/chunks/3kom3ps_bn2q6.js?dpl=nogit-1790362613","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790362613","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790362613","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790362613","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790362613","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790362613","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790362613","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790362613","/_next/static/chunks/440m38krgocdi.js?dpl=nogit-1790362613","/_next/static/chunks/2p6gbbs6zvfpy.js?dpl=nogit-1790362613","/_next/static/chunks/172wsar4r7zzx.js?dpl=nogit-1790362613","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790362613","/_next/static/chunks/3do_93-6buld5.js?dpl=nogit-1790362613","/_next/static/chunks/1pp_uf_jx5j9r.js?dpl=nogit-1790362613","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790362613","/_next/static/chunks/2vg15qyptj-oc.js?dpl=nogit-1790362613","/_next/static/chunks/2b6r02yb2zswo.js?dpl=nogit-1790362613","/_next/static/chunks/12mv6p8rwcl5o.js?dpl=nogit-1790362613","/_next/static/chunks/422ba61wql3d7.js?dpl=nogit-1790362613","/_next/static/chunks/0d2u5k628p_lw.js?dpl=nogit-1790362613","/_next/static/chunks/34ux0fo6f-rm8.js?dpl=nogit-1790362613","/_next/static/chunks/3h4suq-9gmzwh.js?dpl=nogit-1790362613","/_next/static/chunks/0rt2_go1it43r.js?dpl=nogit-1790362613","/_next/static/chunks/0v5zhouho0zlq.js?dpl=nogit-1790362613","/_next/static/chunks/1gtlwpzgzi12z.js?dpl=nogit-1790362613","/_next/static/chunks/2zwoemojbdlmi.js?dpl=nogit-1790362613","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790362613","/_next/static/chunks/3jzaxe43n3e1e.js?dpl=nogit-1790362613","/_next/static/chunks/22z8pa0ys3w4l.js?dpl=nogit-1790362613","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790362613","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790362613","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790362613","/_next/static/chunks/1__39-dgg7p8-.js?dpl=nogit-1790362613","/_next/static/chunks/0pdzmybpnr872.js?dpl=nogit-1790362613","/_next/static/chunks/1zt4k83kx3bkw.js?dpl=nogit-1790362613","/_next/static/chunks/200x0be4hbjpj.js?dpl=nogit-1790362613","/_next/static/chunks/35bn8r0ao86_s.js?dpl=nogit-1790362613","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790362613","/_next/static/chunks/120-bka6zq5lp.js?dpl=nogit-1790362613","/_next/static/chunks/30dopbgd1dkf9.js?dpl=nogit-1790362613","/_next/static/chunks/43ajf4ofaeu5y.js?dpl=nogit-1790362613"],"Gingerbread"] 35:I[647935,["/_next/static/chunks/2msykuvi-vydm.js?dpl=nogit-1790362613","/_next/static/chunks/2mu6-wo6ccpi3.js?dpl=nogit-1790362613","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790362613","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790362613","/_next/static/chunks/0p4rexedanx97.js?dpl=nogit-1790362613","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790362613","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790362613","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790362613","/_next/static/chunks/3lf9kdvvybemj.js?dpl=nogit-1790362613","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790362613","/_next/static/chunks/03q735zs9dbpu.js?dpl=nogit-1790362613","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790362613","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790362613","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790362613","/_next/static/chunks/12xoy6h_w_le6.js?dpl=nogit-1790362613","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790362613","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790362613","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790362613","/_next/static/chunks/32qmkt01ta8b2.js?dpl=nogit-1790362613","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790362613","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790362613","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790362613","/_next/static/chunks/14kf-an-d2n-e.js?dpl=nogit-1790362613","/_next/static/chunks/381o-754ev9ia.js?dpl=nogit-1790362613","/_next/static/chunks/2tr2cll18vqv3.js?dpl=nogit-1790362613","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790362613","/_next/static/chunks/3kom3ps_bn2q6.js?dpl=nogit-1790362613","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790362613","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790362613","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790362613","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790362613","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790362613","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790362613","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790362613","/_next/static/chunks/440m38krgocdi.js?dpl=nogit-1790362613","/_next/static/chunks/2p6gbbs6zvfpy.js?dpl=nogit-1790362613","/_next/static/chunks/172wsar4r7zzx.js?dpl=nogit-1790362613","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790362613","/_next/static/chunks/3do_93-6buld5.js?dpl=nogit-1790362613","/_next/static/chunks/1pp_uf_jx5j9r.js?dpl=nogit-1790362613","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790362613","/_next/static/chunks/2vg15qyptj-oc.js?dpl=nogit-1790362613","/_next/static/chunks/2b6r02yb2zswo.js?dpl=nogit-1790362613","/_next/static/chunks/12mv6p8rwcl5o.js?dpl=nogit-1790362613","/_next/static/chunks/422ba61wql3d7.js?dpl=nogit-1790362613","/_next/static/chunks/0d2u5k628p_lw.js?dpl=nogit-1790362613","/_next/static/chunks/34ux0fo6f-rm8.js?dpl=nogit-1790362613","/_next/static/chunks/3h4suq-9gmzwh.js?dpl=nogit-1790362613","/_next/static/chunks/0rt2_go1it43r.js?dpl=nogit-1790362613","/_next/static/chunks/0v5zhouho0zlq.js?dpl=nogit-1790362613","/_next/static/chunks/1gtlwpzgzi12z.js?dpl=nogit-1790362613","/_next/static/chunks/2zwoemojbdlmi.js?dpl=nogit-1790362613","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790362613","/_next/static/chunks/3jzaxe43n3e1e.js?dpl=nogit-1790362613","/_next/static/chunks/22z8pa0ys3w4l.js?dpl=nogit-1790362613","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790362613","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790362613","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790362613","/_next/static/chunks/1__39-dgg7p8-.js?dpl=nogit-1790362613","/_next/static/chunks/0pdzmybpnr872.js?dpl=nogit-1790362613","/_next/static/chunks/1zt4k83kx3bkw.js?dpl=nogit-1790362613","/_next/static/chunks/200x0be4hbjpj.js?dpl=nogit-1790362613","/_next/static/chunks/35bn8r0ao86_s.js?dpl=nogit-1790362613","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790362613","/_next/static/chunks/120-bka6zq5lp.js?dpl=nogit-1790362613","/_next/static/chunks/30dopbgd1dkf9.js?dpl=nogit-1790362613","/_next/static/chunks/43ajf4ofaeu5y.js?dpl=nogit-1790362613"],"RecordResourceResume"] 36:I[830476,["/_next/static/chunks/2msykuvi-vydm.js?dpl=nogit-1790362613","/_next/static/chunks/2mu6-wo6ccpi3.js?dpl=nogit-1790362613","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790362613","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790362613","/_next/static/chunks/0p4rexedanx97.js?dpl=nogit-1790362613","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790362613","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790362613","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790362613","/_next/static/chunks/3lf9kdvvybemj.js?dpl=nogit-1790362613","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790362613","/_next/static/chunks/03q735zs9dbpu.js?dpl=nogit-1790362613","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790362613","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790362613","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790362613","/_next/static/chunks/12xoy6h_w_le6.js?dpl=nogit-1790362613","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790362613","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790362613","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790362613","/_next/static/chunks/32qmkt01ta8b2.js?dpl=nogit-1790362613","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790362613","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790362613","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790362613","/_next/static/chunks/14kf-an-d2n-e.js?dpl=nogit-1790362613","/_next/static/chunks/381o-754ev9ia.js?dpl=nogit-1790362613","/_next/static/chunks/2tr2cll18vqv3.js?dpl=nogit-1790362613","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790362613","/_next/static/chunks/3kom3ps_bn2q6.js?dpl=nogit-1790362613","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790362613","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790362613","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790362613","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790362613","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790362613","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790362613","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790362613","/_next/static/chunks/440m38krgocdi.js?dpl=nogit-1790362613","/_next/static/chunks/2p6gbbs6zvfpy.js?dpl=nogit-1790362613","/_next/static/chunks/172wsar4r7zzx.js?dpl=nogit-1790362613","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790362613","/_next/static/chunks/3do_93-6buld5.js?dpl=nogit-1790362613","/_next/static/chunks/1pp_uf_jx5j9r.js?dpl=nogit-1790362613","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790362613","/_next/static/chunks/2vg15qyptj-oc.js?dpl=nogit-1790362613","/_next/static/chunks/2b6r02yb2zswo.js?dpl=nogit-1790362613","/_next/static/chunks/12mv6p8rwcl5o.js?dpl=nogit-1790362613","/_next/static/chunks/422ba61wql3d7.js?dpl=nogit-1790362613","/_next/static/chunks/0d2u5k628p_lw.js?dpl=nogit-1790362613","/_next/static/chunks/34ux0fo6f-rm8.js?dpl=nogit-1790362613","/_next/static/chunks/3h4suq-9gmzwh.js?dpl=nogit-1790362613","/_next/static/chunks/0rt2_go1it43r.js?dpl=nogit-1790362613","/_next/static/chunks/0v5zhouho0zlq.js?dpl=nogit-1790362613","/_next/static/chunks/1gtlwpzgzi12z.js?dpl=nogit-1790362613","/_next/static/chunks/2zwoemojbdlmi.js?dpl=nogit-1790362613","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790362613","/_next/static/chunks/3jzaxe43n3e1e.js?dpl=nogit-1790362613","/_next/static/chunks/22z8pa0ys3w4l.js?dpl=nogit-1790362613","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790362613","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790362613","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790362613","/_next/static/chunks/1__39-dgg7p8-.js?dpl=nogit-1790362613","/_next/static/chunks/0pdzmybpnr872.js?dpl=nogit-1790362613","/_next/static/chunks/1zt4k83kx3bkw.js?dpl=nogit-1790362613","/_next/static/chunks/200x0be4hbjpj.js?dpl=nogit-1790362613","/_next/static/chunks/35bn8r0ao86_s.js?dpl=nogit-1790362613","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790362613","/_next/static/chunks/120-bka6zq5lp.js?dpl=nogit-1790362613","/_next/static/chunks/30dopbgd1dkf9.js?dpl=nogit-1790362613","/_next/static/chunks/43ajf4ofaeu5y.js?dpl=nogit-1790362613"],"FlashcardAccessBranch"] 37:I[315438,["/_next/static/chunks/2msykuvi-vydm.js?dpl=nogit-1790362613","/_next/static/chunks/2mu6-wo6ccpi3.js?dpl=nogit-1790362613","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790362613","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790362613","/_next/static/chunks/0p4rexedanx97.js?dpl=nogit-1790362613","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790362613","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790362613","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790362613","/_next/static/chunks/3lf9kdvvybemj.js?dpl=nogit-1790362613","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790362613","/_next/static/chunks/03q735zs9dbpu.js?dpl=nogit-1790362613","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790362613","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790362613","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790362613","/_next/static/chunks/12xoy6h_w_le6.js?dpl=nogit-1790362613","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790362613","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790362613","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790362613","/_next/static/chunks/32qmkt01ta8b2.js?dpl=nogit-1790362613","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790362613","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790362613","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790362613","/_next/static/chunks/14kf-an-d2n-e.js?dpl=nogit-1790362613","/_next/static/chunks/381o-754ev9ia.js?dpl=nogit-1790362613","/_next/static/chunks/2tr2cll18vqv3.js?dpl=nogit-1790362613","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790362613","/_next/static/chunks/3kom3ps_bn2q6.js?dpl=nogit-1790362613","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790362613","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790362613","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790362613","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790362613","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790362613","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790362613","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790362613","/_next/static/chunks/440m38krgocdi.js?dpl=nogit-1790362613","/_next/static/chunks/2p6gbbs6zvfpy.js?dpl=nogit-1790362613","/_next/static/chunks/172wsar4r7zzx.js?dpl=nogit-1790362613","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790362613","/_next/static/chunks/3do_93-6buld5.js?dpl=nogit-1790362613","/_next/static/chunks/1pp_uf_jx5j9r.js?dpl=nogit-1790362613","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790362613","/_next/static/chunks/2vg15qyptj-oc.js?dpl=nogit-1790362613","/_next/static/chunks/2b6r02yb2zswo.js?dpl=nogit-1790362613","/_next/static/chunks/12mv6p8rwcl5o.js?dpl=nogit-1790362613","/_next/static/chunks/422ba61wql3d7.js?dpl=nogit-1790362613","/_next/static/chunks/0d2u5k628p_lw.js?dpl=nogit-1790362613","/_next/static/chunks/34ux0fo6f-rm8.js?dpl=nogit-1790362613","/_next/static/chunks/3h4suq-9gmzwh.js?dpl=nogit-1790362613","/_next/static/chunks/0rt2_go1it43r.js?dpl=nogit-1790362613","/_next/static/chunks/0v5zhouho0zlq.js?dpl=nogit-1790362613","/_next/static/chunks/1gtlwpzgzi12z.js?dpl=nogit-1790362613","/_next/static/chunks/2zwoemojbdlmi.js?dpl=nogit-1790362613","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790362613","/_next/static/chunks/3jzaxe43n3e1e.js?dpl=nogit-1790362613","/_next/static/chunks/22z8pa0ys3w4l.js?dpl=nogit-1790362613","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790362613","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790362613","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790362613","/_next/static/chunks/1__39-dgg7p8-.js?dpl=nogit-1790362613","/_next/static/chunks/0pdzmybpnr872.js?dpl=nogit-1790362613","/_next/static/chunks/1zt4k83kx3bkw.js?dpl=nogit-1790362613","/_next/static/chunks/200x0be4hbjpj.js?dpl=nogit-1790362613","/_next/static/chunks/35bn8r0ao86_s.js?dpl=nogit-1790362613","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790362613","/_next/static/chunks/120-bka6zq5lp.js?dpl=nogit-1790362613","/_next/static/chunks/30dopbgd1dkf9.js?dpl=nogit-1790362613","/_next/static/chunks/43ajf4ofaeu5y.js?dpl=nogit-1790362613"],"TopicFlashcardRunner"] 24:[["$","$L33",null,{"feature":"flashcards"}],"$L34",["$","$L35",null,{"href":"/gcse/maths/aqa/grade-5-5-9-drawing-quadratic-graphs/flashcards","label":"Drawing Quadratic Graphs","subjectCode":"gcse_maths__aqa","surface":"flashcards"}],["$","$L36",null,{"runner":["$","div",null,{"className":"min-h-0 flex-1 overflow-hidden bg-background","children":["$","$L37",null,{"decks":[{"id":"31f86692-985a-e474-9156-b051a6ec61d6","title":"Drawing Quadratic Graphs Flashcards","topicId":"09524d68-b8d8-49c2-911d-cefdbd34faa9","topicSlug":"grade-5-5-9-drawing-quadratic-graphs","cards":[{"id":"8e2bef75-5578-1872-ed8a-7f91319e1afe","cardType":"basic","points":1,"front":"When substituting $x = -3$ into $y = x^2$, what is the resulting value of $y$?","back":"$$9$","mcqOptions":[{"text":"$$9$","correct":true,"explanation":"Substituting gives $y = (-3)^2 = (-3) \\times (-3) = 9$. The product of two negative numbers is positive."},{"text":"$$-9$","correct":false,"explanation":"This comes from applying the square only to $3$ and then retaining the negative sign. The whole value $-3$ is squared, so $(-3)^2 = 9$."},{"text":"$$6$","correct":false,"explanation":"This treats squaring as multiplying the number by $2$. Squaring means multiplying the number by itself, so $(-3) \\times (-3) = 9$."},{"text":"$$-6$","correct":false,"explanation":"This combines doubling with incorrectly retaining the negative sign. The operation is squaring, not doubling, and $(-3)^2$ equals $9$."}]},{"id":"d8a6dc82-0f61-e2e3-42d1-779bf8d5e9df","cardType":"cloze","points":null,"front":"When squaring a negative number, always use [ ] to ensure the result is positive.","back":"When squaring a negative number, always use brackets to ensure the result is positive.","mcqOptions":[{"text":"brackets","correct":true,"explanation":"Brackets show that the negative sign is part of the number being squared. For example, $(-3)^2 = (-3) \\times (-3) = 9$."},{"text":"minus signs","correct":false,"explanation":"A minus sign alone does not ensure the entire negative number is squared. Brackets are required: $(-3)^2 = 9$, whereas $-3^2$ is interpreted as $-(3^2)$."},{"text":"square roots","correct":false,"explanation":"Square roots reverse squaring rather than showing that a negative number is being squared. Brackets enclose the whole negative number, as in $(-3)^2 = 9$."},{"text":"decimal points","correct":false,"explanation":"Decimal points indicate place value and do not control which parts of an expression are squared. Brackets correctly group the negative number, giving $(-3)^2 = 9$."}]},{"id":"ed00fa69-91a0-bac1-0006-1141f29198c7","cardType":"basic","points":1,"front":"What is the specific name for the smooth curve formed by a quadratic graph?","back":"Parabola","mcqOptions":[{"text":"Parabola","correct":true,"explanation":"The graph of a quadratic function is called a parabola. It is a smooth, symmetrical curve that may open upwards or downwards."},{"text":"Hyperbola","correct":false,"explanation":"A hyperbola is associated with relationships such as inverse proportion, not ordinary quadratic functions. The smooth curve formed by a quadratic graph is called a parabola."},{"text":"Ellipse","correct":false,"explanation":"An ellipse is a closed oval-shaped curve and is not the graph of a quadratic function in the form $y = ax^2 + bx + c$. That graph is a parabola."},{"text":"Straight line","correct":false,"explanation":"A straight-line graph represents a linear relationship with no $x^2$ term. A quadratic relationship produces a curved graph specifically called a parabola."}]},{"id":"528e6cde-0224-085a-bab3-0914f3ba109e","cardType":"cloze","points":null,"front":"A quadratic graph opens upwards (like a smile) if the $x^2$ coefficient is [ ].","back":"A quadratic graph opens upwards (like a smile) if the $x^2$ coefficient is positive.","mcqOptions":[{"text":"positive","correct":true,"explanation":"When the coefficient of $x^2$ is positive, increasing $|x|$ makes the quadratic term positive, so the parabola opens upwards like a smile."},{"text":"negative","correct":false,"explanation":"This reverses the relationship between the coefficient’s sign and the graph’s direction. A negative $x^2$ coefficient makes the parabola open downwards; a positive coefficient makes it open upwards."},{"text":"zero","correct":false,"explanation":"If the $x^2$ coefficient is zero, the expression is not quadratic and does not form a parabola. An upward-opening quadratic requires a positive $x^2$ coefficient."},{"text":"squared","correct":false,"explanation":"The variable $x$ is squared, but the coefficient itself need not be a square number. Its sign determines direction: a positive coefficient makes the graph open upwards."}]},{"id":"b6e6b382-010a-3012-c41a-afc23a6567d7","cardType":"cloze","points":null,"front":"A quadratic graph opens downwards (like a frown) if the $x^2$ coefficient is [ ].","back":"A quadratic graph opens downwards (like a frown) if the $x^2$ coefficient is negative.","mcqOptions":[{"text":"negative","correct":true,"explanation":"A negative coefficient of $x^2$ makes the quadratic term decrease as $|x|$ increases, so the parabola opens downwards like a frown."},{"text":"positive","correct":false,"explanation":"This reverses the rule governing the parabola’s direction. A positive $x^2$ coefficient produces an upward-opening graph, while a negative coefficient produces a downward-opening graph."},{"text":"zero","correct":false,"explanation":"A zero $x^2$ coefficient removes the quadratic term, so the graph is no longer a parabola. A downward-opening quadratic must have a negative $x^2$ coefficient."},{"text":"squared","correct":false,"explanation":"The fact that $x$ is squared does not decide whether the graph opens upwards or downwards. The coefficient must specifically be negative for it to open downwards."}]},{"id":"77bd6988-f8b0-51a2-45c9-01c723bff2a3","cardType":"basic","points":1,"front":"How should you join the plotted points when drawing a quadratic graph?","back":"With one smooth curve (do not use a ruler).","mcqOptions":[{"text":"With one smooth curve (do not use a ruler).","correct":true,"explanation":"A quadratic changes gradient continuously, so its plotted points should be connected by one smooth curve. Straight ruler segments would incorrectly introduce sharp changes in gradient."},{"text":"With one straight line (use a ruler).","correct":false,"explanation":"A straight line represents a linear relationship and cannot show the changing gradient of a quadratic. The points should be joined with one smooth curve without using a ruler."},{"text":"With separate unjoined points (do not draw a curve).","correct":false,"explanation":"The plotted points are samples from a continuous quadratic relationship, so leaving them unjoined does not show the complete graph. They should be connected with one smooth curve."},{"text":"With several sharp corners (join each point exactly).","correct":false,"explanation":"Joining points with sharp corners creates piecewise straight sections and sudden gradient changes that a quadratic does not have. The correct graph uses one continuous smooth curve."}]},{"id":"7ccb8e66-2187-8ca6-d390-903b18b073cb","cardType":"basic","points":1,"front":"What is the \"turning point\" of a quadratic graph?","back":"The lowest or highest point of the parabola.","mcqOptions":[{"text":"The lowest or highest point of the parabola.","correct":true,"explanation":"The turning point is where the parabola changes direction. It is the minimum point for an upward-opening parabola or the maximum point for a downward-opening parabola."},{"text":"The leftmost or rightmost point of the parabola.","correct":false,"explanation":"A standard quadratic parabola continues indefinitely to the left and right, so it has no leftmost or rightmost point. Its turning point is its lowest or highest point."},{"text":"The first or second crossing of the x-axis.","correct":false,"explanation":"Crossings of the x-axis are roots, not turning points. The turning point is where the parabola changes direction and reaches its lowest or highest value."},{"text":"The lowest or highest crossing of the y-axis.","correct":false,"explanation":"A quadratic crosses the y-axis only once, and that intercept is not generally an extreme value. The turning point is the parabola’s lowest or highest point."}]},{"id":"b9bbfa3d-e6e0-b4f1-5c1e-7bddf805a790","cardType":"basic","points":1,"front":"How are the \"roots\" of a quadratic identified from its graph?","back":"They are the $x$-values where the curve crosses the x-axis.","mcqOptions":[{"text":"They are the $x$-values where the curve crosses the x-axis.","correct":true,"explanation":"On the x-axis, $y = 0$, so the corresponding $x$-coordinates solve the quadratic equation. These x-axis intersections are therefore the roots of the quadratic."},{"text":"They are the $y$-values where the curve crosses the x-axis.","correct":false,"explanation":"Every point on the x-axis has $y = 0$, so the y-values do not distinguish the roots. The roots are the corresponding $x$-values where the curve crosses the x-axis."},{"text":"They are the $x$-values where the curve crosses the y-axis.","correct":false,"explanation":"The y-axis has $x = 0$, so its intersection gives the y-intercept rather than the roots. Roots are the $x$-values where the curve crosses the x-axis."},{"text":"They are the $x$-values where the curve reaches its turning point.","correct":false,"explanation":"The turning point identifies the parabola’s maximum or minimum, not generally where $y = 0$. Roots are the $x$-values at which the graph crosses the x-axis."}]},{"id":"c4913ec3-46af-dbaf-2994-f335d3d3b260","cardType":"basic","points":1,"front":"At any root on a quadratic graph, what is the value of $y$?","back":"$$0$","mcqOptions":[{"text":"$$0$","correct":true,"explanation":"A root is where the quadratic curve crosses or touches the $x$-axis. Every point on the $x$-axis has a $y$-coordinate of $0$."},{"text":"$$1$","correct":false,"explanation":"This confuses a root with a point one unit above the $x$-axis. At a root, the curve lies on the $x$-axis, so $y=0$."},{"text":"$$-1$","correct":false,"explanation":"A negative $y$-value places the point below the $x$-axis rather than at a root. Roots occur where the curve has $y=0$."},{"text":"$$x$","correct":false,"explanation":"This confuses the variable coordinate with its value at an intercept. A root can have various $x$-coordinates, but its $y$-coordinate is always $0$."}]},{"id":"d433996c-d73e-4809-9873-f466409a0aee","cardType":"cloze","points":null,"front":"In a table of values for a quadratic, the $y$-values usually form a [ ] or a consistent curve.","back":"In a table of values for a quadratic, the $y$-values usually form a symmetrical pattern or a consistent curve.","mcqOptions":[{"text":"symmetrical pattern","correct":true,"explanation":"Quadratic graphs are symmetrical about their vertical axis, so equally spaced $x$-values on opposite sides of that axis produce matching $y$-values."},{"text":"linear pattern","correct":false,"explanation":"A linear pattern has constant first differences and represents a straight line. Quadratic values instead show symmetry and usually have constant second differences."},{"text":"random pattern","correct":false,"explanation":"Quadratic values are determined by a fixed equation, so they are not random. They form a symmetrical pattern around the graph’s vertical axis."},{"text":"alternating pattern","correct":false,"explanation":"Alternating values repeatedly switch according to position, which is not a general property of quadratics. Their $y$-values form a symmetrical pattern around the axis."}]},{"id":"d27e1d66-66d1-ea6a-1f04-c45130871a64","cardType":"basic","points":2,"front":"How do you solve $x^2 - x - 4 = -2$ using the graph of $y = x^2 - x - 4$?","back":"Find the $x$-coordinates where the curve intersects the horizontal line $y = -2$.","mcqOptions":[{"text":"Find the $x$-coordinates where the curve intersects the horizontal line $y = -2$.","correct":true,"explanation":"The curve represents $y=x^2-x-4$, so solutions to the expression equalling $-2$ occur where the curve reaches $y=-2$."},{"text":"Find the $x$-coordinates where the curve intersects the horizontal line $y = 0$.","correct":false,"explanation":"Using $y=0$ would find the roots of $x^2-x-4=0$. Here the expression equals $-2$, so the required horizontal line is $y=-2$."},{"text":"Find the $x$-coordinates where the curve intersects the horizontal line $y = 2$.","correct":false,"explanation":"This loses the negative sign on the right-hand side and would solve $x^2-x-4=2$. The given equation requires intersections with $y=-2$."},{"text":"Find the $x$-coordinates where the curve intersects the vertical line $x = -2$.","correct":false,"explanation":"A vertical line fixes an $x$-value rather than locating where the quadratic has a specified output. Draw the horizontal line $y=-2$ and read the intersection $x$-coordinates."}]},{"id":"e34f810a-1004-c7b2-2941-d5134205c7c8","cardType":"basic","points":2,"front":"What must be done to the equation $x^2 = 3x + 4$ before solving it using the roots of a graph?","back":"Rearrange it to $x^2 - 3x - 4 = 0$ so one side equals zero.","mcqOptions":[{"text":"Rearrange it to $x^2 - 3x - 4 = 0$ so one side equals zero.","correct":true,"explanation":"Subtracting $3x+4$ from both sides gives $x^2-3x-4=0$. The graph’s roots then provide the solutions because roots occur when $y=0$."},{"text":"Rearrange it to $x^2 - 3x + 4 = 0$ so one side equals zero.","correct":false,"explanation":"The constant changes incorrectly here. Subtracting $4$ from both sides produces $-4$, so the correct rearrangement is $x^2-3x-4=0$."},{"text":"Rearrange it to $x^2 + 3x - 4 = 0$ so one side equals zero.","correct":false,"explanation":"Moving $3x$ from the right to the left changes its sign to negative, not positive. The required equation is $x^2-3x-4=0$."},{"text":"Rearrange it to $x^2 - 3x - 3 = 0$ so one side equals zero.","correct":false,"explanation":"This introduces an off-by-one error in the constant term. Subtracting the original $4$ gives $x^2-3x-4=0$, whose roots solve the equation."}]},{"id":"0cd4268f-6c73-0394-a7c8-d2e6f4813145","cardType":"cloze","points":null,"front":"To solve an equation where the quadratic expression equals a number, you must draw or imagine a [ ] at that $y$-value.","back":"To solve an equation where the quadratic expression equals a number, you must draw or imagine a horizontal line at that $y$-value.","mcqOptions":[{"text":"horizontal line","correct":true,"explanation":"A fixed $y$-value is represented by a horizontal line. Its intersections with the quadratic identify the $x$-values for which the expression equals that number."},{"text":"vertical line","correct":false,"explanation":"A vertical line represents a fixed $x$-value, not a fixed output. To solve where the expression equals a number, use a horizontal line at that $y$-value."},{"text":"tangent line","correct":false,"explanation":"A tangent only touches the curve locally and is not generally used to represent a specified output. A fixed $y$-value requires a horizontal line."},{"text":"diagonal line","correct":false,"explanation":"A diagonal line makes $y$ vary with $x$, so it does not represent one fixed value. The correct construction is a horizontal line at the required $y$-value."}]},{"id":"087100b9-7f19-4dc4-cc6d-d7046ddb7790","cardType":"basic","points":2,"front":"For the graph $y = x^2 - 2x - 1$, calculate $y$ when $x = -1$.","back":"$$2$ (calculated as $1 + 2 - 1$)","mcqOptions":[{"text":"$$2$ (calculated as $1 + 2 - 1$)","correct":true,"explanation":"Substituting $x=-1$ gives $(-1)^2=1$ and $-2(-1)=2$. Therefore, $1+2-1=2$."},{"text":"$$-2$ (calculated as $1 - 2 - 1$)","correct":false,"explanation":"This misses that multiplying two negative values gives a positive value: $-2(-1)=2$, not $-2$. The correct calculation is $1+2-1=2$."},{"text":"$$4$ (calculated as $1 + 2 + 1$)","correct":false,"explanation":"This changes the final constant from $-1$ to $+1$. Keeping its original sign gives $1+2-1=2$."},{"text":"$$-4$ (calculated as $-1 - 2 - 1$)","correct":false,"explanation":"This mishandles both $(-1)^2$, which equals $1$, and $-2(-1)$, which equals $2$. The correct result is $1+2-1=2$."}]},{"id":"0f23c1a0-7e0d-b917-e357-4961d045a963","cardType":"basic","points":1,"front":"What is the coordinate of the turning point for $y = x^2 - 4x + 3$ if the lowest point is at $x = 2$ and $y = -1$?","back":"$$(2, -1)$","mcqOptions":[{"text":"$$(2, -1)$","correct":true,"explanation":"Coordinates are written in the order $(x,y)$. With the lowest point at $x=2$ and $y=-1$, the turning point is $(2,-1)$."},{"text":"$$(-1, 2)$","correct":false,"explanation":"This reverses the coordinate order. Since $x=2$ and $y=-1$ at the turning point, the coordinate must be written as $(2,-1)$."},{"text":"$$(2, 1)$","correct":false,"explanation":"This loses the negative sign of the turning point’s $y$-value. The stated lowest point has $x=2$ and $y=-1$, giving $(2,-1)$."},{"text":"$$(-2, -1)$","correct":false,"explanation":"This incorrectly changes the sign of the $x$-coordinate. The turning point is stated to occur at $x=2$, so its coordinate is $(2,-1)$."}]},{"id":"1c87dcca-3c34-908f-7836-5d62006c0192","cardType":"cloze","points":null,"front":"If a quadratic graph has a negative $x^2$ term, the turning point will be the [ ] point on the curve.","back":"If a quadratic graph has a negative $x^2$ term, the turning point will be the highest point on the curve.","mcqOptions":[{"text":"highest","correct":true,"explanation":"A negative coefficient of $x^2$ makes the parabola open downwards. Its turning point is therefore a maximum, meaning it is the highest point on the curve."},{"text":"lowest","correct":false,"explanation":"The lowest turning point occurs when the parabola opens upwards, usually with a positive $x^2$ coefficient. A negative coefficient makes the turning point the highest point."},{"text":"leftmost","correct":false,"explanation":"The sign of the $x^2$ coefficient controls whether the curve opens upwards or downwards, not its horizontal extreme. A negative coefficient gives a highest point."},{"text":"rightmost","correct":false,"explanation":"A standard vertical parabola continues indefinitely in horizontal directions, so its turning point is not a rightmost point. With a negative $x^2$ coefficient, it is the highest point."}]},{"id":"cf16896b-8d30-be18-f63f-07d7c48143c9","cardType":"basic","points":1,"front":"In the coordinate $(x, y)$, which direction does the $x$ value represent?","back":"The horizontal position (across).","mcqOptions":[{"text":"The horizontal position (across).","correct":true,"explanation":"The $x$-coordinate shows how far left or right a point lies from the origin, so it represents the horizontal position."},{"text":"The vertical position (upwards).","correct":false,"explanation":"This confuses the two coordinate axes. The $y$-coordinate gives the vertical position, while the $x$-coordinate gives the horizontal position across the graph."},{"text":"The diagonal position (across).","correct":false,"explanation":"Coordinates do not directly specify a diagonal position. The $x$ value represents horizontal movement across the graph, while the $y$ value represents vertical movement."},{"text":"The vertical position (downwards).","correct":false,"explanation":"The direction of the $y$-axis has been confused with the role of the $x$-axis. The $x$ value represents the horizontal position across the graph."}]},{"id":"60d14c39-e4a9-03e8-b176-565d6e52b3c8","cardType":"cloze","points":null,"front":"If a value in your table of values looks wildly out of place compared to the curve, you should [ ] it.","back":"If a value in your table of values looks wildly out of place compared to the curve, you should recalculate it.","mcqOptions":[{"text":"recalculate","correct":true,"explanation":"An isolated value that does not follow the curve may result from an arithmetic or substitution error, so calculating it again checks and corrects the result."},{"text":"estimate","correct":false,"explanation":"Replacing the value with an estimate could hide the original calculation error. You should recalculate it carefully using the corresponding $x$ value and the quadratic equation."},{"text":"ignore","correct":false,"explanation":"Ignoring an unusual result may leave an incorrect point in the table or graph. You should recalculate it to check for a substitution or arithmetic error."},{"text":"plot","correct":false,"explanation":"Plotting the suspicious value without checking it may distort the quadratic curve. You should recalculate it first to confirm whether the table entry is accurate."}]},{"id":"d8036abf-0ee6-ba6a-9f95-896010a15dd5","cardType":"basic","points":2,"front":"What are the two solutions to $x^2 - x - 4 = 2$ if the graph crosses $y = 2$ at $x = -2$ and $x = 3$?","back":"

$x = -2$
$x = 3$

","mcqOptions":[{"text":"

$x = -2$
$x = 3$

","correct":true,"explanation":"Solutions at a specified $y$ value are the $x$-coordinates of the intersections. The graph meets $y=2$ at $x=-2$ and $x=3$."},{"text":"

$x = -3$
$x = 2$

","correct":false,"explanation":"This reverses the signs associated with the two factors. Solving $x^2-x-6=0$ gives $(x-3)(x+2)=0$, so $x=-2$ and $x=3$."},{"text":"

$x = -2$
$x = 2$

","correct":false,"explanation":"This assumes the intersections are symmetrical about the $y$-axis. The quadratic’s axis of symmetry is $x=0.5$, so the solutions are $x=-2$ and $x=3$."},{"text":"

$x = 2$
$x = 3$

","correct":false,"explanation":"This mistakes the horizontal line’s value, $y=2$, for one of the $x$-coordinates. The actual intersection coordinates give $x=-2$ and $x=3$."}]},{"id":"90f07dea-ce38-06c1-dfd9-60710c55366d","cardType":"basic","points":1,"front":"Why is $y = 7x - x^2$ a \"frown\" shaped graph?","back":"The coefficient of the $x^2$ term is negative.","mcqOptions":[{"text":"The coefficient of the $x^2$ term is negative.","correct":true,"explanation":"A negative coefficient of $x^2$ makes a quadratic open downwards, producing an upside-down U or “frown” shape with a maximum point."},{"text":"The coefficient of the $x^2$ term is positive.","correct":false,"explanation":"A positive coefficient would make the parabola open upwards in a “smile” shape. Here the coefficient is $-1$, so the graph opens downwards."},{"text":"The coefficient of the $x^2$ term is zero.","correct":false,"explanation":"A zero coefficient would remove the quadratic term entirely, producing a straight-line equation. The coefficient is $-1$, which makes the parabola open downwards."},{"text":"The coefficient of the $x^2$ term is 7.","correct":false,"explanation":"This confuses the coefficient of $x$ with the coefficient of $x^2$. The quadratic coefficient is $-1$, and its negative sign creates the frown shape."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Paper 1"},"heading":"Drawing Quadratic Graphs","title":"Drawing Quadratic Graphs Flashcards","topbar":{"backHref":"/gcse/maths/aqa/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"09524d68-b8d8-49c2-911d-cefdbd34faa9","walled":"$L39"}],"$L3a","$L3b"]