shcards","topicId":"7eed228f-ee14-486e-9438-5a6f35366670","topicSlug":"algebra-and-functions-7","cards":[{"id":"3f5d761a-56ef-4712-afe7-c778a6b22793","cardType":"cloze","front":"A quadratic equation has standard form [ ].","back":"A quadratic equation has standard form $ax^2+bx+c=0$, where $a\\neq 0$.","points":null,"mcqOptions":null},{"id":"18c23d77-8492-4ff8-be49-f39013850faf","cardType":"basic","front":"What must you do before identifying $a$, $b$ and $c$ in a quadratic equation?","back":"Rearrange it so one side is zero.","points":1,"mcqOptions":null},{"id":"13583769-039e-4dfa-b902-4b7b3fbc58e9","cardType":"basic","front":"What do the roots of $f(x)=0$ represent on the graph $y=f(x)$?","back":"The $x$-coordinates where the graph meets the $x$-axis.","points":1,"mcqOptions":null},{"id":"ab3dcfbc-e3b6-4a60-9904-1cd2c6e06afd","cardType":"cloze","front":"The zero-product rule states that if $AB=0$, then [ ].","back":"The zero-product rule states that if $AB=0$, then $A=0$ or $B=0$.","points":null,"mcqOptions":null},{"id":"2aaca09f-0b21-4338-abd6-add7b1fdd166","cardType":"basic","front":"When factorising $x^2+bx+c$, what must the two constants multiply to?","back":"They must multiply to $c$.","points":1,"mcqOptions":null},{"id":"2f959413-78f8-4001-8cf5-d98a20f82934","cardType":"basic","front":"When factorising $x^2+bx+c$, what must the two constants add to?","back":"They must add to $b$.","points":1,"mcqOptions":null},{"id":"80f196a0-7814-4962-8326-3364ab8fb787","cardType":"basic","front":"After factorising a quadratic equation, how do you find its roots?","back":"Set each factor equal to zero and solve.","points":2,"mcqOptions":null},{"id":"0a2b4c91-c585-46c5-a502-390819dd0394","cardType":"basic","front":"Solve $6x^2+x-2=0$.","back":"$x=-\\frac{2}{3}$ or $x=\\frac{1}{2}$.","points":2,"mcqOptions":null},{"id":"cdaac2e9-f80a-4321-9962-913f6510cc42","cardType":"cloze","front":"Completing the square uses $x^2+bx=$ $\\text{[...]}$.","back":"Completing the square uses $x^2+bx=$ $\\boxed{\\left(x+\\frac{b}{2}\\right)^2-\\left(\\frac{b}{2}\\right)^2}$.","points":null,"mcqOptions":null},{"id":"6ce0e3e4-5387-4d2e-bfca-8853c0d42f04","cardType":"basic","front":"If $u^2=k$, what values of $u$ must be considered?","back":"$u=\\pm\\sqrt{k}$.","points":1,"mcqOptions":null},{"id":"7e48b717-2228-4ef0-bdc0-fd5341e300e9","cardType":"basic","front":"Solve $x^2+6x-7=0$ by completing the square.","back":"$x=1$ or $x=-7$.","points":2,"mcqOptions":null},{"id":"ea64daeb-bd4b-4cf3-91aa-296d16c6523a","cardType":"cloze","front":"For $ax^2+bx+c=0$, the quadratic formula is $\\text{[...]}$.","back":"For $ax^2+bx+c=0$, the quadratic formula is $\\boxed{x=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}}$.","points":null,"mcqOptions":null},{"id":"c6c2e575-6ef8-4ac0-a4e2-ebd5d52ad2b4","cardType":"basic","front":"Solve $2x^2-3x-1=0$ using the quadratic formula.","back":"$x=\\frac{3\\pm\\sqrt{17}}{4}$.","points":2,"mcqOptions":null},{"id":"3b4f9ab4-157c-438a-a6c5-b97ddc2afb40","cardType":"cloze","front":"The discriminant of $ax^2+bx+c=0$ is $\\text{[...]}$.","back":"The discriminant of $ax^2+bx+c=0$ is $\\boxed{\\Delta=b^2-4ac}$.","points":null,"mcqOptions":null},{"id":"2e443c75-5992-449b-b172-2e0aa6681890","cardType":"basic","front":"What does $\u0002Delta>0$ imply about a quadratic equation?","back":"It has two distinct real roots.","points":1,"mcqOptions":null},{"id":"c25e38b9-8330-42eb-ac00-004bc29e3729","cardType":"basic","front":"What does $\u0002Delta=0$ imply about a quadratic equation?","back":"It has one repeated real root.","points":1,"mcqOptions":null},{"id":"82746914-57ae-4314-84c8-2a5268c6bc66","cardType":"basic","front":"What does $\u0002Delta<0$ imply abou

1.1.6 Algebra and functions Flashcards

1.1.6 Algebra and functions Flashcards