r touches the x-axis.","points":1},{"id":"5fa5484d-c459-4ff6-beff-6c473e0a42ba","cardType":"basic","front":"How do the roots of a quadratic function help solve an inequality?","back":"They split the number line into regions where the expression is either positive or negative.","points":2},{"id":"8909a7ca-196b-4963-96b9-e34ded5d5666","cardType":"cloze","front":"A quadratic with a positive leading coefficient forms a U-shaped curve called a [ ].","back":"A quadratic with a positive leading coefficient forms a U-shaped curve called a parabola.","points":null},{"id":"d9486159-2654-4d7c-8066-12a16aeca898","cardType":"basic","front":"For an upward-opening parabola, where is the quadratic negative ($<0$)?","back":"Between the two roots.","points":1},{"id":"e702aa4f-f104-4eb4-8bd7-d03cfb72e518","cardType":"basic","front":"For an upward-opening parabola, where is the quadratic positive ($>0$)?","back":"Outside the two roots (the two separate tails).","points":1},{"id":"22dcafd5-c91d-432d-906c-bba81604da89","cardType":"cloze","front":"If the inequality sign is $\\le$ or $\\ge$, the final solution must [ ] the boundary roots.","back":"If the inequality sign is $\\le$ or $\\ge$, the final solution must include the boundary roots.","points":null},{"id":"5dd801c7-a72f-4ba2-9496-c55b8331e3ff","cardType":"basic","front":"Why is it incorrect to write $x < -5$ and $x > -2$ as one combined inequality?","back":"They represent two separate regions on the number line; they must be joined by \"or\".","points":2},{"id":"b9de1d2c-f4fc-48e4-b79d-e3826b2615a1","cardType":"basic","front":"What must you do to the inequality sign when multiplying or dividing by a negative number?","back":"Reverse the direction of the sign.","points":1},{"id":"7690cb28-6f99-48a5-86c4-e251a0733d77","cardType":"cloze","front":"To solve a quadratic inequality, first rearrange it into [ ] (where one side is zero).","back":"To solve a quadratic inequality, first rearrange it into standard form (where one side is zero).","points":null},{"id":"351c3b08-ca02-4880-8ecb-d2c28c18c124","cardType":"basic","front":"Solve $x^2 \\le 64$.","back":"$$-8 \\le x \\le 8$","points":2},{"id":"8e2cd10a-9c24-4834-bcf6-2eedc1852daa","cardType":"cloze","front":"Solving $x^2 \\le 64$ by writing only $x \\le 8$ is a mistake because it ignores [ ] that also square to 64.","back":"Solving $x^2 \\le 64$ by writing only $x \\le 8$ is a mistake because it ignores negative values that also square to 64.","points":null},{"id":"d17554a4-6fc7-4c6d-bee1-dfd609d8e570","cardType":"basic","front":"How do you solve a quadratic inequality that cannot be factorised?","back":"

Use the quadratic formula to find the roots.
Determine the region (inside/outside).
Estimate values if integers are required.

","points":3},{"id":"ab53365c-b30d-499a-99c9-07039f51bf82","cardType":"basic","front":"Which integers satisfy $1.59 < x < 4.41$?","back":"2, 3, and 4.","points":1},{"id":"e36ad57f-3c50-4be8-a046-42853f9834d8","cardType":"basic","front":"What does it mean if a quadratic has no real roots in the context of an inequality?","back":"The graph never crosses the x-axis; it is either always positive or always negative.","points":2},{"id":"c90971dd-0f47-43a5-8244-2deefb160a15","cardType":"basic","front":"How do you check a quadratic with no roots to see if it satisfies $f(x) > 0$?","back":"Test a single value

Quadratic Inequalities Flashcards

Quadratic Inequalities Flashcards

Quadratic Inequalities Flashcards

Quadratic Inequalities Flashcards