Free Printable Unit 9: Solving Quadratic Equations Unit Test

1.

Solve the equation by factoring.

a)

A. x = 9 and x = 6

b)

B. x = 9 and x = -6

c)

C. x = 54 and x = 18

d)

D. x = -9 and x = 6

2.

a)

A. Add 16 to both sides of the equation.

b)

B. Subtract 9 from both sides of the equation.

c)

C. Take the square root of 9.

d)

D. Add 64 to both sides of the equation.

3.

a)

A. I, III and IV

b)

B. III and IV

c)

C. IV only

d)

D. I, II, III and IV

4.

a)

A. Lauryn

b)

B. Keenan

c)

C. Both students

d)

D. Neither student

5.

Which of the following represents the positive solution to the equation?

a)

A. x = 1

b)

B. x = 0.2

c)

C. x = 1.5

d)

D. x = 3.2

6.

A system of equations is shown below. Find the solution(s) to the system of equations. Write as ordered pairs.

(a)

7.

(a)

Choose from the below words

REGGIE

KILEY

EDUARDO

8.

What is the vertex of (x + 9)² − 5 = 20? Write as an ordered pair.

(a)

9.

What are the solutions to (x + 9)² − 5 = 20? Check all that apply.

a)

-14

b)

-4

c)

8

d)

4

e)

-8

10.

Pedro is analyzing the quadratic function y = x² – 6x + 20. Which of the following is NOT true?

a)

A. An equivalent function is y = (x – 3)² +11.

b)

B. The function has a minimum at -3.

c)

C. The vertex of the function is (3, 11).

d)

D. The function will have no x-intercepts.

11.

Three students wrote quadratic equations. Use the discriminant to determine which student(s) wrote equations with two real solutions.

a)

A. Maria only

b)

B. Zaida only

c)

C. Maria and Erick

d)

D. Maria, Erick, and Zaida

12.

What are the solutions to x² + 13x = -40?

(a)

13.

Solve the equation below.

(a)

14.

Convert the quadratic function shown below to vertex form using the steps of completing the square.

a)

A. y = (x + 4)² + 10

b)

B. y = (x + 8)² + 38

c)

C. y = (x + 4)² + 42

d)

D. y = (x +8)² + 26

15.

Use the discriminant to determine the number of real solutions to the system of equations shown below.

(a)

16.

Mr. Bailey writes the quadratic equation shown below on the board. Which of the following statements is true?

a)

A. The discriminant is 0, therefore the related quadratic function has one x-intercept.

b)

B. The discriminant is 0, therefore the related quadratic function has no x-intercepts.

c)

C. The discriminant is -6, therefore the solutions to the equation are imaginary numbers.

d)

D. The discriminant is -6, therefore there are two real solutions to the equation.

17.

Write the quadratic equation that represents the function.

a)

A. y = x² – x – 2

b)

B. y = 4x² – 4x – 8

c)

C. y = 4x² – 8

d)

D. y = 4x² + 4x – 8

18.

Find the sum of roots in the equation given.

(a)

19.

What's the first step in completing the square for the equation below?

a)

Isolate all the variable terms on one side.

b)

Add 6 to both sides

c)

Divide everything by 2

d)

Factor the left side.

20.

What do you do next in this problem for square root method?

a)

Divide by 3

b)

Square root both sides

c)

Factor

d)

Divide "b" by 2 and square it

21.

Write an equation with the roots given..

22.

Find the product and sum of roots for the equation below.

a)

-6

b)

8

c)

3

d)

4

23.

Find the product of roots for the equation given.

(a)

24.

Graph $y=\left(x-3\right)^2-4$

25.

A quadratic functions is defined as:

$f\left(x\right)=\left(x-4\right)^2+3$

What is the equation of the parabola in standard form?

(a)

Choose from the below words

$f\left(x\right)=x^2-8x^2+19$

$f\left(x\right)=x^2-8x-13$

$f\left(x\right)=x^2-4x+19$

$f\left(x\right)=x^2-4x-13$

$f\left(x\right)=x^2+8x+19$

26.

A quadratic is defined as $y=\left(x+3\right)^2-6$

What is the equation for this function in standard form?

Your answer needs to be in the form of:

$y=ax^2+bx+c$

Enter your answer in the space provided.

27.

You need to know the vertex to state the (a) which comes from the x value of your vertex.

You also need to know the Vertex to state the (b) which comes from the y value of your vertex.

Choose from the below words

Axis of Symmetry

Range

a

y-intercept

Domain

28.

What is the positive solution to this equation? $2x^2-5x=12$

29.

Match each option to the types of solutions produced

a)

$\frac{-3\pm\sqrt[]{9-4\left(1\right)\left(-3\right)}}{2\left(1\right)}$

1.

Irrational Solutions

b)

$\frac{-3\pm\sqrt[]{9-\left(4\right)\left(1\right)\left(3\right)}}{2\left(1\right)}$

2.

Complex Solutions

c)

$\frac{-3\pm\sqrt[]{9-4\left(1\right)\left(2\right)}}{2\left(1\right)}$

3.

Rational Solutions

30.

Solve the equation:

$\left(x+5\right)^2=81$

Enter the larger solution only.

31.

What is the positive solution of $x^2-2x=80$ ?

32.

Evaluate b² - 4ac if a=4 and b=-3 and c=2

a)

x = -35

b)

x = 35

c)

x = 23

d)

x = -23

33.

Identify a, b and c in the quadratic equation: $2x^2-3x-5=0$

a)

a = 2 , b = 3, c = -5

b)

a = 2, b = -3, c = 5

c)

a = 2, b = -3, c = -5

d)

a = -2, b = 3, c = 5

34.

$b^2-4ac$ is called the . . .

a)

Square root

b)

Quadratic formula

c)

X-intercepts

d)

Discriminant

35.

Solutions of a quadratic equation are also called

a)

roots

b)

x-intercepts

c)

zeros

d)

All of the above

36.

If there are no real solutions, the discriminant is

a)

zero

b)

a postive number

c)

a negative number

d)

a perfect square

37.

If there is one solution, the discriminant is . . .

a)

zero

b)

a postive number

c)

a negative number

d)

a perfect square

38.

If the discriminant is equal to -2, how many solutions are there?

a)

2 Imaginary Solutions

b)

1 Real Solution

c)

2 Real Solutions

d)

Infinite Solutions

39.

Solve the following equation using the quadratic formula: $5x^2-6=13x$

a)

$x=-2,\ x=-\frac{3}{5}$

b)

$x=2,\ x=\frac{3}{5}$

c)

$x=3,\ x=-\frac{2}{5}$

d)

undefined

40.

Complete the Square
x² + 10x + ____

a)

x² + 10x - 100

b)

x² + 10x + 100

c)

x² + 10x - 25

d)

x² + 10x + 25

41.

What value of c would complete the square?

x² +8x + c

a)

4

b)

16

c)

64

d)

-16

42.

Complete the Square:

x² + 14x + (a)

43.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

44.

Factor the perfect square trinomial
x² + 14x + 49

a)

(x+7)²

b)

(x+7)(x-7)

c)

(x-7)²

d)

(x+14)²

45.

Match the following

a)

x² + 16x + 64 =

1.

(x + 8)²

b)

x² - 16x + 64 =

2.

(x - 8)²

c)

x² + 8x + 16 =

3.

(x + 4)²

d)

x² + 4x + 4 =

4.

(x + 2)²

e)

x² - 4x + 4 =

5.

(x -2)²

46.

Put the steps to Completing the Square in the correct order

a)

Move constants to one side

b)

add $\left(\frac{b}{2}\right)^2$ to both sides

c)

Factor the trinomial

d)

Take the square root of both sides.

e)

Solve both cases.

1)

2)

3)

4)

5)

47.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

48.

Solve for x by taking the Square Root:

(x+6)²= 49

a)

x = 7 and 12

b)

x = ±7

c)

x = 1 and -13

d)

x = 43 and -55

Unit 9: Solving Quadratic Equations Unit Test

Total questions: 48

Worksheet time: 2hrs 36mins

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