Free Printable Chapter 4 Review

Worksheets

Chapter 4 Review

Total questions: 52

Worksheet time: 13hrs 32mins

Name

Class

Date

Solve: x² -121= 0

x = 10, 11

x= 11, -11

x = 12, 10

x = 10, -10

Solve by factoring: x² +14x +48 = 0

x = -8, 6

x = -4, -8

x = 8, 6

x = -8, -6

Solve by factoring: 3x² +3x = 60

x = -5, 4

x = -5, -4

x = 5, -4

x = 5, 4

Solve by factoring: 4x² = 36

x = 9, -9

x = 3, -3

x = 9, 3

x = 9, -4

Solve by factoring: 3x² -14x - 24 = 0

x = 4/3, x = 6

x = -2, 4

x = -4/3, 6

x = 2, -4

Solve by factoring: 6x² - 23x = -20

x = 5/2, x = 4/3

x = -5/2, 4/3

x = 5, 4

x = 5, -4

Solve by factoring: 4x² +14x + 6 = 0

x = -2, -12

x = 2, 12

x = -1, -3

x = -1/2, -3

Solve by factoring: x² = 15x - 56

x = -7, -8

x = 7, 8

x = 7, -8

x = -7, 8

Solve by factoring: 5x² -80 = 0

x = 16, -16

x = 4, -4

x = 8, -8

x = 2, -2

10.

Solve by factoring: 5x² +13x - 28 = 0

x = -7, 20

x = 7, -20

x = 4, -7/5

x = -4, 7/5

11.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

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

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

a = 4, b = 8, c = 3

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

12.

Use the quadratic formula to solve 2x² + 2x - 12?

-2, 3

2, 3

2, -3

-2, -3

13.

Identify the 'b' value: y = 16x² -8x -24

-8

-24

14.

Identify the 'a' value: y = 16x² -8x -24

-8

-24

15.

Solve using the quadratic formula.
2x² - 9x - 35 = 0

x = 7/2, x = -6

x = -5/2, x =5

x = -3/7, x =6

x = -5/2, x = 7

16.

Solve using the quadratic formula:
4x²+ 4x + 1 = 0

x = -½

x = -2

x = 0

17.

Solve Using the Quadratic Formula
x² + 4x - 40 = -8

-10 & -4

-4 & 10

-8 & 4

8 & -4

18.

Identify the 'c' value: y = 16x² -8x -24

-8

-24

19.

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

square it

divide it by 2 and square the result

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

divide it by 2 only

20.

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

21.

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

-7

-4

-3

22.

Solve the following equation by completing the square:
n² - 2n - 3 = 0

{3 and-1}

{4 and -4}

{5 and -3}

{8 and -7}

23.

Solve the following equation by completing the square:
n² = 18n + 40

{11 and -11}

{16 and 2}

{20 and -2}

{10 and -4}

24.

Solve by completing the square:
k² − 12k + 23 = 0

{6 + √13, 6 - √13}

{-6 + √13, -6 - √13}

{6 + √59, 6 - √59}

{-6 + √59, -6 - √59}

25.

Complete the square for
x² + 12x + ____

x² + 12x + 144

x² + 12x + 36

x² + 12x - 36

x² + +12x - 144

26.

Complete the square.
x² + 6x + ____

x² + 6x + 9

x² + 6x - 36

x² + 6x + 36

x² + 6x - 9

27.

Complete the square.
x² + 14x + ____

x² + 14x - 196

x² + 14x + 49

x² + 14x - 49

x² + 14x + 196

28.

Complete the Square
x² + 10x + ____

x² + 10x - 100

x² + 10x + 100

x² + 10x - 25

x² + 10x + 25

29.

Solve by completing the square.
y² + 10y = -9

1 and -12

-1 and -9

1 and -9

1 and -1

30.

The length of a rectangle is 6 meters more than the width. The area is 72 square meters. Find the length and width.

Length = 6, Width = 12

Length = 18, Width = 4

Length = 12, Width = 6

Length = 4, Width = 6

31.

A dolphin jumps from the water at at initial velocity of 16 feet per second. The equation h = -8t² + 16t models the dolphin's height at any given time, t. What is the maximum height the dolphin jumps?

1 foot

5 feet

7 feet

8 feet

12 feet

32.

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?

2 ft

80 ft

144 ft

64 ft

33.

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. When does the maximum height occur?

6 seconds

3 seconds

145 seconds

160 seconds

34.

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. When does the rocket hit the ground?

7 seconds

6 seconds

3 seconds

8 seconds

35.

When I want to find the maximum or minimum height of an object, I should_____.

Set the equation = 0 and solve.

Use x = (-b/2a) as my answer.

Substitute x = 0 into the equation.

Find the y-coordinate for the vertex.

36.

A raft is dropped from a helicopter 256 feet in the air above the ocean. Its approximate height, h, after t seconds is given by the function h(t) = -16t² + 256. How many seconds did it take the raft to hit the water?

-4

37.

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

(5, -4)

(-5, -4)

(-15, -4)

(15, -4)

38.

Which of the following is the correct equation for the given graph?

f(x) = (x - 2)² - 1

f(x) = (x + 2)² - 1

f(x) = -(x + 2)² - 1

f(x) = -(x - 2)² - 1

39.

Which of the following is the correct equation for the given graph?

f(x) = -(x + 2)² - 4

f(x) = -(x - 2)² - 4

f(x) = -3(x - 2)² - 4

f(x) = -3(x + 2)² - 4

40.

What is the green dashed line called?

roots or x-intercepts

parabola

axis of symmetry

line of dashes

41.

What is the equation of this graph?

f(x) = (x -5)² + 1

f(x) = (x - 1)² - 5

f(x) = (x + 1)² - 5

f(x) = (x + 5)² +1

42.

What is the axis of symmetry for the following parabola?

f(x) = -2(x - 3)² + 1?

x=-3

x=3

x=1

y=3

43.

Does the equation have a max or min?
y = 2x² + 7x + 5

max

min

44.

What is the y-intercept?
f(x) = -2x² + 4x - 6

(0, 6)

(0, -6)

(6, 0)

(-6, 0)

45.

What is the axis of symmetry?
f(x) = x²- 8x + 15.

x = -4

x = 4

y = 4

y = -4

46.

What is the vertex?
f(x) = -x²- 4x + 12.

(-2, 16)

(2, 0)

(2, 4)

(-2, 4)

47.

What is the vertex of y=x²+4x+3?

(2,1)

(-2,1)

(0,0)

(-2,-1)

48.

The discriminant is

aX² + bX + c

b - 4ac

b² - 4ac

b² + 4ac

49.

If the discriminant is positive, how many solutions and of what type?

1 real solution

2 real solutions

2 complex solutions

50.

What is the following called? b²-4ac

Axis of symmetry

Quadratic Formula

Vertex

Discriminant

51.

Find the discriminant of the quadratic equation:
2x² + 10x - 15 = 0

-20

220

52.

How many solutions does the equation 4x² + 4x + 1 = 0 have?

More than 2

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Chapter 4 Review

Total questions: 52

Worksheet time: 13hrs 32mins

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