Free Printable Chapter 10 review

1.

What form is the quadratic equation written in?
y = (x - 2)(x + 4)

a)

Factored

b)

Standard

c)

Vertex

d)

Descending Polynomial

2.

For $y=3\left(x+1\right)\left(x-5\right)$ , find the roots/zeros/solutions/x-intercepts.

a)

x = -1, 5

b)

x = -5, 1

c)

x = -3, 15

d)

x = -15, 3

e)

This equation has no real roots

3.

What is the vertex of the function f(x) = 2(x + 7)(x - 5)

a)

(1, -64)

b)

(1, 64)

c)

(-1, 72)

d)

(-1, -72)

4.

What is the vertex of the function y = -8(x - 3)² - 5

a)

(-3, 5)

b)

(3, -5)

c)

(-3, -5)

d)

(3, 5)

5.

Give the coordinates for the vertex of $y=-2x^2+4x+1$ as an ordered pair.

a)

(1, 3)

b)

(-1, 3)

c)

(-4, -1)

d)

(1, 4)

e)

(4, -1)

6.

Rewrite y = -2(x+5)² in standard form

a)

y = -2x²-50

b)

y = -2x² - 20x -50

c)

y = 2x² - 20x -50

d)

y = -2x² + 20x -50

7.

Rewrite y = 6(x+4)² - 19 in standard form

a)

y = 6x² - 13

b)

y = 6x² +48x + 77

c)

y = 6x² +16x -3

d)

None of these

8.

Rewrite y = 8(x -3)² - 15 in standard form

a)

y = 8x² - 24x + 57

b)

y = 8x² + 57

c)

y = 8x² - 6x + 57

d)

y = 8x² - 48x + 57

9.

Rewrite y = x² + 12x + 7 in vertex form

a)

y = (x+6)² + 7

b)

y = (x+6)² + 43

c)

y = (x+6)² - 29

d)

None of these

10.

Rewrite y = x² - 16x + 12 in vertex form

a)

y = (x - 8)² + 76

b)

y = (x - 16)² + 76

c)

y = (x - 8)² + 4

d)

None of these

11.

Rewrite y = 6x² - 48x + 37 in vertex form

a)

y = 6(x-4)² - 59

b)

y = 6(x-4)² + 133

c)

y = 6(x+4)² - 59

d)

None of these

12.

Rewrite y = 12x² + 120x + 139 in vertex form

a)

y = 12(x+10)²+ 39

b)

y = 12(x+5)²+ 439

c)

y = 12(x+5)²- 161

13.

The flight of a pumpkin that was launched by Cole Edins is represented by the equation y = -.0013(x - 179)² + 52, where x represents the horizontal distance traveled in feet and y represents the height of the pumpkin in feet. HOW HIGH ABOVE THE GROUND WAS THE PUMPKIN AFTER IT TRAVLED 357.2 FEET?

a)

13.78 ft

b)

8.19 ft

c)

6.11 ft

d)

10.72 ft

14.

Greyson DeJulio hits a long fly ball off Zach Thompson's 35 mph "fastball" during BP. The ball leaves his bat 3 feet above the ground and reaches its maximum height of 48 feet after traveling a horizontal distance of 192 feet. The left field fence is 365-feet from home plate and is 8 feet high. Did Greyson's bomb clear the fence? If so, by how much? If not, how much did it miss by?

4 lines

15.

The quadratic equation h = -16t² + 80t gives the time t in seconds when a golf ball is at a height of 0 feet. How do you find how many seconds until the ball is at its maximum height?

a)

Find the x-coordinate of the maximum

b)

find the y-coordinate of the maximum

c)

find the zero

d)

Use the table to find the y-intercept

e)

find the x-intercept

16.

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

17.

Makenna Baker dropped a water balloon over the side of the roof at EHS in the hopes of hitting Klein in the head. Unfortunately she missed and it hit the ground. from a height of 30 feet. The approximate height of the balloon at any point during its fall can be represented by the following quadratic equation, where h is the height of the balloon and t is the time in seconds since the balloon was dropped. h = -16t² + 50 About how long did it take for the balloon to hit the ground?

a)

1.73 seconds

b)

1.37 seconds

c)

2.45 seconds

d)

2.83 seconds

18.

Determine if the point (2, 0) is a solution to the following system:
$y=2x-4$
$y=x^2-4$

a)

Yes, because it works in only one equation.

b)

Yes, because it works in both equations.

c)

No, because it works in neither equation.

d)

No, because it works in only one equation.

19.

What are the solutions to the system:
y = x² + 3x - 5
y = x + 3

a)

(-4, 2) and (-1, 5)

b)

(-4, -1) and (2, 5)

c)

(2, -1 and (-4, 5)

d)

(-4, 1) and (2, -1)

20.

Is the point (2, 7) a solution to this nonlinear system?

a)

Yes a solution

b)

No Not a solution

21.

Is the point (5, 3) a solution to this nonlinear system?

a)

Yes a solution

b)

No Not a solution

22.

Find the solution:
y = x² - 4x + 6
y = x + 2

a)

(3, 1) and (6, 4)

b)

(-1, 1) and (4, 2)

c)

(1, 3) and (4, 6)

d)

(1, 4) and (3, 6)

23.

Find the solution(s): y = 5x² - 9x -16

y = x + 24

a)

(4, 28)

b)

(-4, 20) and (2, 26)

c)

(4, 28) and (-2, 22)

d)

(1, 4) and (3, 6)

24.

What is the measure of angle 1?

a)

120

b)

40

c)

30

d)

60

25.

What is the measure of arc QP?

a)

140

b)

40

c)

70

d)

100

26.

$m\angle ABC=$

a)

100 degrees

b)

50 degrees

c)

200 degrees

d)

160 degrees

27.

Find the value of x.

a)

$127.2\degree$

b)

$31.8\degree$

c)

$63.6\degree$

28.

Find the measure of arc QR

a)

106

b)

85

c)

113

d)

78

29.

All the inscribed angles that form intercepted arc AZ have the same measure?

a)

TRUE

b)

FALSE

30.

What is the measure of angle 2?

a)

80

b)

45

c)

125

d)

40

31.

What is the value of x?

a)

58

b)

119

c)

61

d)

90

32.

Solve for the value of x

a)

35⁰

b)

54⁰

c)

70⁰

d)

178⁰

33.

Find the standard form of $y=3\left(x+1\right)\left(x-5\right)$ .

a)

$y=3x^2-12x-15$

b)

$y=x^2-4x-5$

c)

$y=3x^2+12x-15$

d)

$y=3x^2-4x-5$

34.

Write $y=-2x^2+4x+1$ in vertex form.

a)

$y=-2\left(x-1\right)^{2\ }+3$

b)

$y=\left(x+1\right)^2+3$

c)

$y=-2\left(x-4\right)^2+1$

d)

$y=4\left(x-1\right)^2-2$

35.

Which of the following is Standard Form?

a)

$y=ax^2+bx+c$

b)

$y=a\left(x-p\right)\left(x-q\right)$

c)

$y=a\left(x-h\right)^2+k$

36.

Which of the following is Vertex Form?

a)

$y=ax^2+bx+c$

b)

$y=a\left(x-p\right)\left(x-q\right)$

c)

$y=a\left(x-h\right)^2+k$

37.

What is an equation of a parabola with the vertex of $\left(3,-4\right)$ ?

a)

$y=-\frac{1}{2}\left(x+3\right)^2-4$

b)

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

c)

$y=\frac{3}{2}\left(x-3\right)^2-4$

d)

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

38.

What is an equation of a parabola with the vertex of $\left(-2,-4\right)$ ?

a)

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

b)

$y=\frac{3}{2}\left(x-2\right)^2+4$

c)

$y=\frac{3}{2}\left(x-2\right)^2-4$

d)

$y=\left(x+2\right)^2+4$

39.

What is an equation of a quadratic with x-intercepts at $\left(-1,0\right)$ and $\left(-10,0\right)$

a)

$y=-2\left(x+1\right)\left(x-10\right)$

b)

$y=\frac{1}{3}\left(x+1\right)\left(x+10\right)$

c)

$y=-\frac{1}{10}\left(x-1\right)\left(x+10\right)$

d)

$y=3\left(x-1\right)\left(x-10\right)$

40.

Convert

f(x) = 3(x - 5)² - 1

to standard form.

a)

f(x) = 3x²-30x + 74

b)

f(x) = 3x²-10x + 24

c)

f(x) = 3x²-30x + 24

d)

f(x) = 3x²-30x + 75

41.

Convert

f(x) = 2(x - 2)² +9

to standard form.

a)

f(x) = 2x² + 8x + 9

b)

f(x) = 2x² - 8x - 4

c)

f(x) = 2x² - 8x + 17

d)

f(x) = 2x² - 8x + 8

42.

A quadratic equation has a vertex form of y = -2(x - 1)² - 2. Which of the following is equivalent to this form?

a)

y = 2x² - 4x + 4

b)

y = -2x² + 4x - 4

c)

y = -2x² - 4x + 4

d)

y = 2x² + 4x - 4

43.

Convert
y = 3(x+1)² - 8 into standard form.

a)

y=3x² + 6x - 5

b)

y=3x² - 6x - 5

c)

y=3x² + 6x + 5

d)

y=3x² - 6x + 5

44.

Convert the equation y = x²- 2x - 5 into vertex form.

a)

y = (x - 1)²- 6

b)

y = -(x - 1)²- 6

c)

y = (x + 1)²- 6

d)

y = -(x + 6)²- 1

45.

Which of the following shows

f(x) = x² + 12x - 2

written in vertex form?

a)

f(x) = (x + 6)² + 142

b)

f(x) = (x + 6)² - 34

c)

f(x) = (x + 6)² - 38

d)

f(x) = (x + 6)² + 34

46.

Fill in the blank: When we convert from standard to vertex form, the a value will ____________.

a)

Stay the same

b)

Be the same but negative

c)

Become the vertex

d)

Be squared

47.

What is the equation of the graph below?

a)

f(x ) = I x + 4 I + 2

b)

f(x ) = -I x - 4 I + 2

c)

f(x ) = I x - 4 I + 2

d)

f(x ) = -I x + 4 I + 2

48.

What is the equation of the absolute value function?

a)

f(x)= 4|x+3|

b)

f(x)= 1/4 |x+3|

c)

f(x)= 1/4 |x - 3|

d)

f(x)= 4|x - 3|

49.

Write the equation of the circle.

a)

(x+1)² + (y +1)² = 3

b)

(x+1)² + (y -1)² = 3

c)

(x+1)² + (y +1)² = 9

d)

(x-1)² + (y -1)² = 9

50.

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

a)

4

b)

2

c)

3

d)

16

51.

In the equation (x-4)²+(x-3)²=25, the radius is

a)

4

b)

3

c)

5

d)

25

52.

In the equation
(x-3)²+(y-2)²=16, the center of the circle is...

a)

(3,2)

b)

(-3, -2)

c)

(-2, -3)

d)

(2, 3)

53.

Write the equation of a circle with center
(7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

54.

What is the radius of the circle
(x+7)²+(y-2)²=144?

a)

7

b)

12

c)

13

55.

What is the equation for this circle?

a)

(x+1)+(y+1)=9

b)

x²+y²=9

c)

x+y=9

56.

Write the equation of a circle with center (7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

57.

Does the point (4,5) lie on the circle whose center is (-2,-2) and radius 9?

a)

yes

b)

No

58.

Is the point (3 , 5) inside, outside or on the circle with equation x² + y² = 9?

a)

Inside the Circle

b)

Outside the Circle

c)

On the Circle

59.

Write the equation of a circle with center (h,k) and radius r.

a)

x² + y² = r²

b)

(x + h)² + (y + h)² = r²

c)

(x - h)² + (y - k)² = r²

d)

(x - h)² - (h - k)² = r

60.

The point (-5,6) is on a circle with center (-1,3) write the equation of the circle

a)

(x+1)² + (y-3)²= 4000

b)

(x+5)² + (y-0)²= 25

c)

(x+1)² + (y-3)²= 25

d)

(x-1)² + (y+3)²= 25

61.

What is the correct inequality for this graph?

a)

y < |x+4| -3

b)

y ≤ |x+4|+ 3

c)

y ≤ |x-4| -1

d)

y < 1/2|x+4| + 1/2

62.

What is the correct inequality for this graph?

a)

y > -|x| + 7/2

b)

y > -2|x| + 4

c)

y > -1/2|x| + 2

d)

y > |x| + 4

63.

What is the correct inequality for this graph?

a)

y ≤ 2|x-1| - 1

b)

y ≤ 1/2|x-1| + 4

c)

y ≥ -2|x+1| - 2

d)

y ≥ -2|x-1| + 1

64.

Which graph matches the inequality?

a)

b)

c)

d)

65.

Is the line for the inequality

f(x) ≥|x+3|- 9 going to solid or dotted?

a)

Dotted

b)

Solid

66.

Are we going to shade above or below for f(x) ≤|x|+1?

a)

Above

b)

Below

67.

Which inequality is shown?

a)

y< -x²

b)

y≤ -x²

c)

y> -x²

d)

y≥ -x²

68.

Which inequality is represented by the graph?

a)

y > (x - 3)² - 3

b)

y ≥ (x + 3)² - 3

c)

y > (x + 3)² - 3

d)

y ≥ (x - 3)² - 3

69.

Which inequality is represented by the graph?

a)

y > -(x - 4)² + 1

b)

y > -(x - 1)² + 4

c)

y < (x - 4)² + 1

d)

y > (x + 4)² + 1

70.

a)

y ≤ (x - 3)² + 3

b)

y < (x + 3)² - 3

c)

y < (x - 3)² - 3

d)

y ≤ (x + 3)² - 3

71.

Which correctly shows the inequality $y<\left(x+4\right)^2+1$ ?

a)

b)

c)

d)

72.

How many solutions does this system of equations have?

(a)

73.

Type the first step to solve this system using substitution:

y=-5x

2x+6y=-3

a)

2x + 6(-5x) = -3

b)

2x - 5x = -3

c)

y + 6(-5y) =-3

d)

2(-5x) + 6y = -3

74.

Which of the following best represents a system of equations with no solution?

a)

b)

c)

d)

75.

At which point do the graphs of 2x = y + 5 and 6x + 2y = -5 intersect?

a)

(2, -4)

b)

(-4, 1)

c)

(1/2, -4)

d)

(-3/2, -8)

76.

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

a)

f(x) = -(x + 2)² - 4

b)

f(x) = -(x - 2)² - 4

c)

f(x) = -3(x - 2)² - 4

d)

f(x) = -3(x + 2)² - 4

77.

If the blue graph is
f(x) = x²
then the red must be...

a)

g(x) = x²- 5

b)

g(x) = x²+ 5

c)

g(x) = (x - 5)²

d)

g(x) = (x + 5)²

78.

What is the radius of the circle with this equation x²+y²-10x+8y-23=0?

a)

4

b)

2

c)

8

79.

What is the center for the circle with this equation x² + y² + 2x - 8y - 10 = 0?

a)

(-2,8)

b)

(2,7)

c)

(-1,4)

80.

Determine the equation of the circle in standard form: x²+ y²+ 6x - 12y + 20 = 0

a)

(x-3)² + (y+6)² = 25

b)

(x+3)² + (y-6)² = 25

c)

(x-3)² + (y+6)² = 45

d)

(x+3)² + (y-6)² = 5

81.

Determine the center and radius:
x²+ y²- 10x + 8y -8 = 0

a)

C = (5,-4) r = 7

b)

C = (-5,4) r = 7

c)

C = (-4,5) r = 49

d)

C = (5,-4) r = 49

82.

Determine the center and radius: x²+ y²+ 14x - 2y = -1

a)

center= (-7,2) radius= 3

b)

center= (-7,1) radius= 7

c)

center= (-4,1) radius= 5

83.

Determine the equation of the circle in standard form:
x² + y² + 4x + 6y - 36 = 0

a)

(x+2)² + (y+3)² = 49

b)

(x+2)² + (y+3)² = 13

c)

(x-2)² + (y-3)² = 49

d)

(x-2)² + (y-3)² = 13

Chapter 10 review

Total questions: 83

Worksheet time: 6hrs 51mins

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