Free Printable Solving Quadratics Review (H)

1.

Which of the following are methods to solve quadratics (select all that apply)?

a)

Difference of Squares

b)

Completing the Square

c)

Square Roots

d)

Grouping

2.

Which method of solving quadratics would you use to solve the following:

$12x^2-7\ =41$

a)

Factoring when a = 1

b)

Completing the Square

c)

Factoring when a > 1

d)

Square Roots

3.

For which method of solving do you need to apply the Zero Product Property?

a)

Factoring

b)

Difference of Squares

c)

Square Roots

d)

Completing the Square

4.

If the solutions to your quadratic are $\pm3$ what does that say about the quadratic and its graph? (Select all that apply)

a)

The axis of symmetry is the y-axis

b)

The parabola has TWO x-intercepts

c)

The parabola has ONE x-intercept

d)

The quadratic did not have a b-term

5.

Solve

3x² - 192 = 0

a)

-32 or 32

b)

No Solution

c)

-8 or 8

d)

-64 or 64

6.

Solve (4x + 3)(x - 6) = 0

a)

x = {-3/4, 6}

b)

x = {-3, 6}

c)

x = {3/4, -6}

d)

x = -3/4, -6}

7.

Solve a² + 10a - 24 = 0

a)

a = {2, -12}

b)

a = {4, 6}

c)

a = {-12, 2}

d)

a = {-6, -4}

8.

What is the degree of every Quadratic Equation?

a)

1

b)

2

c)

3

d)

4

9.

What is the greatest number of solutions that a Quadratic Equation can have?

a)

0

b)

1

c)

2

d)

3

10.

Solve the equation using the zero product property.
3x ( 2x - 4) = 0

a)

x = -1/3 or x = -2

b)

x = 0 or x = 2

c)

x = 0 or x = -2

d)

x = -1/3 or x = 2

11.

Mike solved the equation x² + 8x = 14 by completing the square. Which of the following equations is part of the correct solution.

a)

(x + 4)² = 14

b)

x² + 8x - 14 = 0

c)

(x + 4)² = 30

d)

x² + 8x + 4 = 18

12.

Simplify √50

a)

5√10

b)

10√5

c)

5√5

d)

5√2

13.

What value of "c" would create a

perfect square trinomial?

x² + 10x + _____ = 17

a)

c = 20

b)

c = 100

c)

c = 25

d)

c = 10

14.

Simplify 4√75

a)

4√5

b)

12√5

c)

20√3

d)

7√3

15.

Choose all that are perfect square trinomials.

a)

$x^2+4x\ +\ 4\ =\ 25$

b)

$x^2-6x+16\ =11$

c)

$x^2+2x+1=49$

d)

$x^2+8x+7=0$

16.

Which formula do you use to find the "c-value" that makes a quadratic a perfect square trinomial?

a)

$b^2-4ac$

b)

$y=x^2$

c)

$\left(\frac{b}{2}\right)^2$

d)

$\frac{-b}{2a}$

17.

Which of the following are the correct solutions to the quadratic:

$x^2-10x+49=4x+1$

a)

x = {-7, 7}

b)

x = {6, 8}

c)

x = {-8, -6}

d)

x = {-12, -4}

18.

What is one of the solutions to this equation?
(2x - 1)² = 49

a)

7

b)

-7

c)

-4

d)

-3

19.

Determine the values of

a, b, and c for

the quadratic equation:

4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

20.

If the discriminant is 75, which of the following could be its graph? Choose all that apply.

a)

b)

c)

d)

e)

21.

Find the discriminant:

$9x^2+6x+1=0$

22.

Which property do you need when solving a quadratic by factoring?

a)

Distributive Property

b)

Zero Product Property

c)

Commutative Property

d)

Associative Property

23.

Which are way to solve a quadratic? Choose all that apply.

a)

FOIL

b)

graphing

c)

factoring

d)

Zero Product Property

24.

How many solutions can a quadratic have? Choose all that apply.

a)

One

b)

None

c)

Two

d)

Infinite

25.

To solve using square roots, your quadratic must be in which format?

a)

x = -b/2a

b)

ax² + bx = 0

c)

ax² + bx + c = 0

d)

ax² + c = 0

26.

Find the value of "c" that makes the following quadratic a perfect square trinomial: x² - 12x + c = 0

(Show work for credit)

a)

144

b)

-144

c)

36

d)

-36

27.

Which of the following equations is quadratic?

a)

y = x³ + 1

b)

x + 10x = 4x²

c)

3x - 2 = y

d)

y = 3(2)^x

28.

What is the relationship of the axis of symmetry to the solutions of a quadratic?

a)

Axis of symmetry and quadratic solutions have no relationship

b)

Axis of symmetry falls halfway between the solutions

c)

Axis of symmetry divides your parabola into two equal halves

d)

Axis of symmetry and quadratic solutions are the same

29.

Solve for x:

36x² = 9

a)

x = ± 1/4

b)

x = ± 9/36

c)

x = ± 1/2

d)

No real solution(s)

30.

What is the first step in solving for x?
(x + 6)²= 49

a)

Subtract 6 from both sides

b)

Take the square root of both sides

c)

Add 6 to both sides

d)

Foil $\left(x+6\right)^2$

31.

Solve for x:

x² = -216

a)

$x=\pm6\sqrt[]{6}$

b)

$x=\pm\sqrt[]{216}$

c)

$x=\pm\sqrt[]{-216}$

d)

No Solution(s)

32.

Solve by taking square roots:

(x + 1)² = 25

a)

$x=4$

b)

$x=\pm4$

c)

$x=\left\{-6,\ 4\right\}$

d)

No solution(s)

33.

Which is equivalent to $\pm7$ ?

a)

{0, 7}

b)

{0, -7}

c)

(-7, 7}

d)

{7}

34.

In order to solve using square roots, what must be true?

a)

There must be factors of the c-term that add/subtract to the b-term

b)

Equation must be set equal to zero

c)

All terms must be perfect squares

d)

No b-term

35.

Find the vertex for y = 2(x + 4)² - 2

a)

(4, 2)

b)

(-4, -2)

c)

(4, -2)

d)

(-4, 2)

36.

Which method of solving would you use to solve the following:

$12x^2-7\ =41$

a)

Factoring

b)

Quadratic Formula

c)

Graphing

d)

Square Roots

37.

If the solutions to your quadratic are $\pm3$ what are your x-intercepts?

a)

x = {-3, 3}

b)

(0, -3) and (0, 3)

c)

(-3, 0) and (3, 0)

38.

Solve the equation using the zero product property.
3x ( 2x - 4) = 0

a)

x = -1/3 or x = -2

b)

x = 0 or x = 2

c)

x = 0 or x = -2

d)

x = -1/3 or x = 2

39.

What is the standard form for a Quadratic?

a)

ax²+ bx = - c

b)

x = -b ± √(b²-4ac) / 2a

c)

ax² + bx + c

d)

y = mx + b

40.

Which is a factor of x² - 3x - 28?

(Show work for credit)

a)

x + 7

b)

x - 14

c)

x + 4

d)

x - 4

Solving Quadratics Review (H)

Total questions: 40

Worksheet time: 1hrs 25mins

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