Free Printable Quadratics Test Review

1.

If given the equation

y = 3(x + 5)² - 4, what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

2.

What is the axis of symmetry for the following equation?

y=3x²-6x+5

a)

x=-6

b)

x=1

c)

x=-1

d)

x=2

3.

John throws a ball upward at a speed of 40 feet per second from a platform that is 20 feet high. The height of the ball is given by the function h(t) = -16t² + 40t + 20, where t is the time in seconds. What is the maximum height that the ball reaches?

a)

A. 45 ft.

b)

B. 50 ft.

c)

C. 60 ft.

d)

D. 55 ft.

4.

Find the axis of symmetry of

y=5\left(x+3\right)^2-4

a)

$x=-3$

b)

$x=3$

c)

$x=-4$

d)

$x=4$

5.

Find the vertex of

y=-\frac{1}{2}\left(x+11\right)^2-4

a)

$\left(-11,-4\right)$

b)

$\left(11,-4\right)$

c)

$\left(11,4\right)$

d)

$\left(-11,4\right)$

6.

Is the graph concave up or down?

f(x) = -(x + 3)² - 5

a)

concave up

b)

concave down

7.

Find the axis of symmetry for
f(x) = 2x²- 8x + 15.

a)

x = -4

b)

x = 2

c)

y = 4

d)

y = -4

8.

What is the vertex?

a)

(2, 4)

b)

(3, -1)

c)

(0, 8)

d)

(4, 2)

9.

Does this graph have a maximum or minimum value?

a)

maximum

b)

minimum

c)

neither

d)

both

10.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

11.

What is the vertex of the function
f(x) = -x²+8x-10?

a)

(4,6)

b)

(4,38)

c)

(-4, -10)

d)

(8, -10)

12.

A ball is thrown into the air with an upward velocity of 40ft/s. Its height h in feet after t seconds is given by the function :

h(t) = -16t² + 40t + 10

How many seconds does it take the ball to reach its maximum height?

a)

1.25 seconds

b)

1.4 seconds

c)

2.5 seconds

d)

2 seconds

13.

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation

s(t) = –16t² + 64t + 80

What will be the object's maximum height?

a)

2 ft

b)

80 ft

c)

144 ft

d)

64 ft

14.

The point in which a graph hits the x-axis is know as the _____

a)

Solution

b)

x-intercept

c)

Root

d)

All answers are correct

15.

Identify the vertex and whether the graph opens up or down.

a)

(-1, 4); opens up

b)

(-1, 4); opens down

c)

(1, 4); opens up

d)

(1, 4); opens down

16.

Does the following quadratic equation have a maximum or minimum value? How can you tell?
y=x²+2x-3

a)

Minimum value, because the a value is positive

b)

Maximum value, because the b value is positive

c)

Maximum value, because the a value is positive

d)

Minimum value, because the c value is negative

17.

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

18.

Solve:
2x² - 9x = 35

a)

x = 7/2, x = -6

b)

x = -5/2, x =5

c)

x = -3/7, x =6

d)

x = -5/2, x = 7

19.

Solve:
4x²= -4x -1

a)

x = -½

b)

x = -2

c)

x = 0

20.

a)

A

b)

B

c)

C

d)

D

21.

a)

-3, 4

b)

3, 4

c)

-4, -3

d)

-3

22.

Solve using the quadratic formula

a)

A

b)

B

c)

C

d)

D

23.

Find the zeros.

a)

0 and 4

b)

0 and -4

c)

0

d)

-4

24.

What are the solutions to this equation? (x-3)(x+2)=0

a)

x=3,-2

b)

x=-3,2

c)

x=2,3

d)

x=3,2

25.

Solve using any method.

x² + 4x= 12

a)

x = 2 and -2

b)

x = -6 and 2

c)

x = 6 and -2

d)

x = 1 and -1

26.

Solve the equation using any method:

4x²+2x - 6 = 0

a)

x = 1 & -1.5

b)

x = -1 & 1.5

c)

x = (-2 ±√92)/8

d)

x = (-2 ± √100)/8

27.

Solve:
x² - 49 = 0

a)

x = -7, x = 7

b)

x = -7

c)

x = 7

d)

x = -7, x = 1

28.

Convert x²- 9x + 20 = 0 to factored form and solve.

a)

(x-10)(x+2); x = -2, 10

b)

(x+4)(x+5); x = -5, -4

c)

(x-4)(x-5); x = 4, 5

d)

Not factorable

29.

What are the roots / zeros / solutions of the equation
$x^2-14x+48=0$ ?

a)

-6\ and\ -8

b)

$-6\ and\ 8$

c)

$6\ and\ -8$

d)

$6\ and\ 8\$

30.

$The\ solutions\ of\ 2x^2-8x\ =\ 0\ are$

a)

$-2\ and\ \ 2$

b)

$0,\ -2,\ and\ \ 2$

c)

$0\ and\ -4$

d)

$0\ and\ 4$

31.

$Given:\ \ x^2-10x\ +\ 21\ =\ 0$

What are the solutions of the equation

a)

$1\ \ and\ \ 21$

b)

$-5\ \ and\ \ 5$

c)

$3\ \ and\ \ 7$

d)

$-3\ \ and\ \ -7$

32.

Solve the quadratic function using any method. Select the solutions.
$x^2+4x=12$

a)

x = 2

b)

x = -6

c)

x = 6

d)

x = 1

e)

x = -2

33.

Lisa solves the equation below:

x² + 4x - 12 = 2

(x - 2)(x + 6) = 2,

by setting x -2 = 0 and x + 6 = 0.

Her solutions are x = 2 and x = -6.

Is Lisa correct? Why or why not?

a)

Yes, she factored correctly.

b)

Yes, she factored correctly and then square rooted.

c)

No, she did factor correctly, but solved it wrong. It should be equal to 2

d)

No, she didn't set the equation to zero.

34.

What is the vertex of this parabola?

a)

(−1, 3)

b)

(−3, 11)

c)

(−2, 5)

d)

(0, 5)

35.

How many solutions does this graph have?

a)

one

b)

two

c)

no solutions

d)

cannot be determined

36.

Members of the math club launch a model rocket from ground level with an initial velocity of 96 ft/sec. This can be modeled with the function h(t) = -16t² + 96t. What is the range of the function?

a)

0 ≤ y ≤ 145

b)

y ≤ 145

c)

0 ≤ x ≤ 6

d)

All Reals

37.

What is the equation of this graph?

a)

f(x) = (x -5)² + 1

b)

f(x) = (x - 1)² - 5

c)

f(x) = (x + 1)² - 5

d)

f(x) = (x + 5)² +1

38.

Find the zeros of this quadratic.

a)

b=4/5, b=3

b)

b=4, b=-3

c)

b=1/5, b=3

d)

b=4/5, b=-3

39.

Which Formula is the Discriminant Formula?

a)

b)

c)

d)

40.

If the Discriminant is >0 How many real solutions will you have?

a)

1

b)

2

c)

3

d)

0

41.

If the Discriminant is =0 How many real solutions will you have?

a)

1

b)

2

c)

3

d)

0

42.

If the Discriminant is < 0, How many real solutions will you have?

a)

1

b)

2

c)

3

d)

0

43.

If there are 2 real solutions, which value can be the discriminant?

a)

13

b)

0

c)

-7

44.

If there is 1 real solution, which value can be the discriminant?

a)

13

b)

0

c)

-7

45.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

46.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

47.

If the graph of a quadratic does not touch the x-axis at any point, then it has:

a)

1 Real Solution

b)

2 Real Solutions

c)

Half a Solution

d)

No Real Solution / Imaginary solutions

48.

$For\ 2x^2\ -\ 4x\ +\ 3\ =\ 0,\ which\ is\ correct?$

a)

$\frac{4\ \pm\sqrt{-16\ -4\left(2\right)\left(3\right)}}{2\left(2\right)}$

b)

$\frac{-4\ \pm\sqrt{16\ -4\left(2\right)\left(3\right)}}{2\left(2\right)}$

c)

$\frac{4\pm\sqrt{16-4\left(2\right)\left(3\right)}}{4}$

d)

$\frac{4\pm\sqrt{40}}{4}$

49.

if a = 2, b = 4 and c = 10, what are the errors in

\frac{4\ \pm\sqrt{16\ -\ 4\left(2\right)\left(-10\right)}}{2}

a)

The 4 outside the radical should be negative.

b)

The denominator should be 4, not 2.

c)

10 should be positive and not negative.

d)

All of the above

50.

Solve

2x^2+4x\ +10=0

Simplify answers

a)

$-4\ \pm8i$

b)

$-1\pm2i$

c)

$\frac{-4\ \pm8i}{4}$

d)

$\pm8i$

51.

(2+3i)(4-2i)

a)

14+8i

b)

48+16i

c)

12-8i

d)

2-8i

52.

What is the simplified form of (-9 + 5i) + (3 -2i)

a)

-12 + 31i

b)

-6 + 3i

c)

-11 + 7i

d)

5 - 3i

53.

What is the simplifies form of (11 - 7i) - (-3 + 12i)

a)

8 - 19i

b)

8 + 5i

c)

13- 19i

d)

14 -19i

54.

Simplify.

a)

-5i

b)

5

c)

5i

d)

-5

55.

Simplify √-45

a)

3i√5

b)

-3i√5

c)

-i√45

d)

45i

56.

Find the conjugate of:
5 + 7i

a)

5 − 7i

b)

-5 − 7i

c)

-5 + 7i

57.

What is the simplified form of $(8-3i)^2$

a)

$73$

b)

$16-6i$

c)

$55+48i$

d)

$55-48i$

58.

What is the simplified form of $(-6i)(3i)$

a)

$-18$

b)

$-18i$

c)

$18$

d)

$-18i^2$

59.

What is the simplified form of $(-3+2i)(1-4i)$

a)

$-2-2i$

b)

$5+14i$

c)

$-11-10i$

d)

$-3-8i$

60.

What is the simplified form of $(11-7i)-(-3+12i)$

a)

$8-19i$

b)

$8+5i$

c)

$13-19i$

d)

$14-19i$

61.

What is the simplified form of $(-9+5i)+(3-2i)$

a)

$-12+31i$

b)

$-6+3i$

c)

$-11+7i$

d)

$5-3i$

62.

Find the best fitting quadratic model for the data given.

a)

$1.2x^2+13x+504.3$

b)

$12x^2+13x+504.3$

c)

$0.12x^2+1.3x+504.3$

63.

Which Quadratic equation best represents the table?

a)

$y=-2.7x+7.4$

b)

$y=0.95x^2-2.08x-0.75$

c)

$y=-.05x-3.26$

d)

$y=0.95x^2+2.08x+0.75$

64.

The function below represents the flight of a ball being thrown by a girl who is standing on a box. What is the maximum height of the ball?
y = -1/2x² + 2x + 2?

a)

2 feet

b)

About 5 feet

c)

0 feet

d)

4 feet

65.

Find the best fitting Quadratic model for the data

a)

$-0.26x^2-17.3x+222.8$

b)

$-0.26x2^2+22.59x+23.02$

c)

$2.6x^2+22.9x+20.03$

d)

$2.6x^2+2.3x+23.02$

66.

In a number line, what does it represent?

a)

Greater than -2 but less than 6

b)

greater than 6 but less than -2

c)

Greater or equal to -2 but less that or equal to 6

d)

Greater or equal to 6 but less than or equal to -2

67.

Which correctly shows the inequality $y>x^2+4x+6$ ?

a)

b)

c)

d)

68.

Is the point (2, 1) a solution to the inequality shown?

a)

Yes

b)

No

69.

Which correctly shows the inequality $y\ge-x^2+2x+1$ ?

a)

b)

c)

d)

70.

Test the point (0, 0). Is the solution area inside or outside the parabola for the inequality $y>-2x^2-8x-7$ ?

a)

Inside

b)

Outside

c)

Neither

71.

Which correctly shows the inequality $y<x^2-6x+13$ ?

a)

b)

c)

d)

72.

Determine the number of solutions to the given linear-quadratic system.

a)

0 solutions

b)

1 solution

c)

2 solutions

d)

3 solutions

73.

What are the solutions to the graphed system?

a)

(0,-2) and (-3,1)

b)

(-2,0) and (2,0)

c)

(0,-2) and (3,1)

d)

(2,2) and (1,0)

74.

Solve the system of linear and quadratic equations:

y = 5

y = 2x² - 16x + 29

a)

(6, 5) and (2, 5)

b)

(2, 6)

c)

(6, 2)

d)

(5, 6) and (5, 2)

75.

How many solutions does this system of equations have?

a)

one solution

b)

two solutions

c)

no solutions

d)

All of the above

76.

Determine the solution to the given linear-quadratic function.

a)

(0, 0)

b)

(3, 0)

c)

(2, -3)

d)

(-3, 2)

77.

a)

A

b)

B

c)

C

d)

D

Quadratics Test Review

Total questions: 77

Worksheet time: 6hrs 59mins

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