Quadratic Equations flashcards

30 practice cards drawn from the Quadratic Equations lessons. Tap a card to turn it over. Every answer is checked against the lesson it came from.

Read the Quadratic Equations lessons in full →

Solve x² − 9x + 18 = 0

x = 3 or x = 6

from “Solving by Factoring”

Solve (x − 2)(x − 5) = 0

x = 2 or x = 5

from “Solving by Factoring”

For x² + 5x − 2, what is b² − 4ac?

33

from “The Quadratic Formula”

For x² + 3x − 1, what is b² − 4ac?

13

from “The Quadratic Formula”

The roots of x² + 8x + 2 = 0 are α and β. What is α + β?

-8

from “The Sum and Product of the Roots”

The roots of x² − 8x + 3 = 0 are α and β. What is αβ?

3

from “The Sum and Product of the Roots”

A quadratic has b² − 4ac = −4. How many real roots?

0

from “The Discriminant and the Nature of the Roots”

A quadratic has b² − 4ac = 1. How many real roots?

2

from “The Discriminant and the Nature of the Roots”

Is x² + 2x − 2 always positive, always negative, or does it change sign?

changes sign

from “Always Positive or Always Negative Quadratics”

Is x² + 1x + 2 always positive, always negative, or does it change sign?

always positive

from “Always Positive or Always Negative Quadratics”

x² + 10x + ? completes the square. What is the missing number?

25

from “Completing the Square”

x² + 6x + ? completes the square. What is the missing number?

9

from “Completing the Square”

The vertex of y = (x − 3)² + 4

(3, 4)

from “Sketching from Vertex and Factored Form”

Where does y = (x − 5)(x + 6) cross the x-axis?

5 and −6

from “Sketching from Vertex and Factored Form”

Which move turns x + b/2a = ±√(b² − 4ac)/2a into the formula?

take b/2a from both sides

from “Deriving the Quadratic Formula”

(x + b/2a)² = b²/4a² − c/a. Over the bottom 4a², what is the right side?

(b² − 4ac)/4a²

from “Deriving the Quadratic Formula”

A rectangle is x by x + 3 with area 18. What is x?

3

from “Forming Quadratic Equations”

A rectangle is x by x + 3 with area 70. What is x?

7

from “Forming Quadratic Equations”

Solve (x − 3)(x − 6) < 0

3 < x < 6

from “Solving a Quadratic Inequality”

Solve x² − 8x + 12 > 0

x < 2 or x > 6

from “Solving a Quadratic Inequality”

y = x² and y = 8x − 15 meet where x = 3. What is y there?

9

from “A Linear Equation Paired with a Quadratic”

y = x² and y = 7x − 10 meet where x = 5. What is y there?

25

from “A Linear Equation Paired with a Quadratic”

Does y = 2x − 2 meet y = x² twice, once, or not at all?

not at all

from “When a Line Meets, Touches or Misses a Curve”

Does y = 4x − 6 meet y = x² twice, once, or not at all?

not at all

from “When a Line Meets, Touches or Misses a Curve”

Multiply 15/x = x − 2 by x. What do you get?

15 = x² − 2x

from “Fractional Equations”

Multiply 6/x = x − 1 by x. What do you get?

6 = x² − 1x

from “Fractional Equations”

Squaring √(x + 7) = x − 5 gives x = 2 or x = 9. Which one holds?

x = 9

from “Solving Equations with a Square Root”

Squaring √(x + 6) = x − 6 gives x = 3 or x = 10. Which one holds?

x = 10

from “Solving Equations with a Square Root”

Solve (x − 3)/(x − 7) < 0

3 < x < 7

from “Solving a Rational Inequality”

Solve (x − 2)/(x − 4) < 0

2 < x < 4

from “Solving a Rational Inequality”

Practice these in the app — your progress saves there.