Free Printable Alg2H Unit 2 Test Practice

1.

Look at the system of equations.

y = x² - 4x + 6

y = x + 2

What is the solution set for the system of equations?

a)

{(3, 1), (6, 4)}

b)

{(-1, 1), (4, 2)}

c)

{(1, 3), (4, 6)}

d)

{(1, 4), (3, 6)}

2.

Look at the system of equations.

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

$y=-x^2+2x+7$

What is the solution set for the following system of equations?

a)

{(-3,-8), (2,7)}

b)

{(-3,-20), (2,5)}

c)

{(3,16), (-2,-9)}

d)

{(3,10), (-2,-11)}

3.

What is the vertex for
f(x)=4(x-2)² + 3

a)

(-2, 3)

b)

(2,-3)

c)

(4,3)

d)

(2,3)

4.

Does the parabola
f(x)=4(x-2)² + 3
open up or down?

a)

up

b)

down

5.

What is the axis of symmetry for
f(x)=4(x-2)² + 3

a)

4

b)

2

c)

x = -2

d)

x = 2

6.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

7.

What is the vertex of the parabola: y=2(x-3)²+4

a)

(3,4)

b)

(-3,4)

c)

(3, -4)

d)

(-3,-4)

8.

What is the vertex form of a quadratic function?

a)

f(x) = 2a(x-h)² + k

b)

f(x) = a(x-h)² + k

c)

f(x) = (x+h)² + k

d)

f(x) = a(x-h) - k

9.

What steps transform the graph y = x² to y = 2(x+2)² - 5?

a)

Compress by 2, shifted 2 units left and 5 down

b)

Stretch by 5, shifted 5 units left and 2 down

c)

Stretch by 2, shifted 2 units left and 5 down

d)

Compress by 5, shifted 2 units left and 2 down

10.

What steps transform the graph y = x² to y = x² + 8

a)

shifted up 8 units

b)

shifted down 8 units

c)

shifted left 8 units

d)

shifted right 8 units

11.

What steps transform the graph y = x² to y = (x-4)²

a)

Shifted down 4 units

b)

Shifted left 4 units

c)

Shifted right 4 units

d)

Shifted up 4 units

12.

Identify the vertex of this quadratic:

$y=\frac{1}{2}\left(x-7\right)^2+7$

a)

$\left(-7,\ -7\right)$

b)

$\left(7,\ 7\right)$

c)

$\left(7,\ -7\right)$

d)

$\left(-7,\ 7\right)$

13.

What steps transform the graph y = x² to y = 1/2(x+2)² - 5?

a)

Compress by 1/2 , shifted 2 units left and 5 down

b)

Stretch by 5, shifted 5 units left and 2 down

c)

Stretch by 2, shifted 2 units left and 5 down

d)

Compress by 5, shifted 1/2 units left and 2 down

14.

What is the vertex and how does it transform the graph?

$y=\frac{1}{8}\left(x+4\right)$

a)

(-4, 0) and it will shift the graph left 4

b)

(4, 0) and it will shift the graph right 4

c)

(1/8, 0) and it will shift the graph up 1 and over 8

d)

(4, 0) and it will shift the graph up 4 and over 1

15.

Which equation in vertex form matches the quadratic graph?

a)

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

b)

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

c)

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

d)

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

16.

Which equation in vertex form matches the quadratic graph?

a)

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

b)

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

c)

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

d)

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

17.

Which equation in vertex form matches the quadratic graph?

a)

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

b)

$y=-\frac{1}{2}x^2$

c)

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

d)

$y=-x^2-1$

18.

A parabola has a vertex at (-3,2).
Where is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

19.

Write y = x² + 4x - 1 in vertex form.

a)

y = (x - 2)² + 5

b)

y = (x + 2)² - 5

c)

y = (x + 2)² - 1

d)

y = (x +2)² + 3

20.

What is the range of the function:

$f\left(x\right)=4\left(x-3\right)^2+1$

a)

$y\ge3$

b)

$y\ge1$

c)

$y\le1$

d)

$y\le3$

21.

What is the range of the function:

$f\left(x\right)=-6\left(x+1\right)^2+5$

a)

$y\le5$

b)

$y\ge5$

c)

$y\le-6$

d)

$y\ge-6$

22.

What is the range of the function:

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

a)

$y\ge-4$

b)

$y\le-4$

c)

$y\ge4$

d)

$y\le4$

23.

Find the zeros

$f\left(x\right)=-3x^2+18x-15$

a)

$x=1,\ x=-5$

b)

$x=-1,\ x=-5$

c)

$x=1,\ x=5$

d)

$x=-1,\ \ x=5$

24.

Find the zeros

$f\left(x\right)=x^2+10x+16$

a)

$x=2,\ x=-8$

b)

$x=-2,\ x=-8$

c)

$x=-2,\ x=8$

d)

$x=2,\ \ x=8$

25.

Find the zeros

$f\left(x\right)=4x^2+16x-48$

a)

$x=-2,\ x=6$

b)

$x=2,\ x=6$

c)

$x=-2,\ x=-6$

d)

$x=2,\ \ x=-6$

26.

Find the zeros

$f\left(x\right)=6x^2-7x-5$

a)

$x=-\frac{5}{3},\ x=\frac{1}{2}$

b)

$x=\frac{5}{3},\ x=-\frac{1}{2}$

c)

$x=-\frac{5}{3},\ x=-\frac{1}{2}$

d)

$x=\frac{5}{3},\ \ x=\frac{1}{2}$

27.

Find the zeros

$f\left(x\right)=3x^2+10x-8$

a)

$x=\frac{2}{3},\ x=-4$

b)

$x=\frac{2}{3},\ x=4$

c)

$x=-\frac{2}{3},\ x=-4$

d)

$x=-\frac{2}{3},\ \ x=4$

28.

Find the vertex

$f\left(x\right)=x^2+2x-15$

a)

$\left(2,-11\right)$

b)

$\left(-2,11\right)$

c)

$\left(1,16\right)$

d)

$\left(-1,-16\right)$

29.

What's the equation of the AOS?

$f\left(x\right)=-x^2+6x+91$

a)

$x=3$

b)

$x=-1$

c)

$x=5$

d)

$x=-7$

30.

$y=-5(x+2)^2-10$
Convert the equation from vertex form to standard form.

a)

y = -5x²- 20x - 30

b)

y = -5x²- 4x - 10

c)

y = 25x² + 100x + 90

d)

y = 25x² - 10x - 30

31.

$y=-3(x+5)^2-4$
Convert the equation from vertex form to standard form.

a)

y = 9x²- 15x + 21

b)

y = -3x²- 75x - 4

c)

y = 9x²+ 90x + 221

d)

y = -3x²- 30x - 79

32.

Which quadratic function in vertex form can be represented by the graph that has a vertex at (3,-7) and passes through the point (1,-10)?

a)

b)

c)

d)

33.

Which function is best represented by this graph?

a)

b)

c)

d)

34.

Write the equation of the quadratic function that has a vertex of (-5, 9) and passes through the point (-7, -15).

a)

y = 6(x + 5)² + 9

b)

y = -6(x - 5)² + 9

c)

y = 6(x - 5)² + 9

d)

y = -6(x + 5)² + 9

35.

What is the equation in vertex form?

a)

y = 4(x + 3)² - 4

b)

y = -4(x - 3) - 4

c)

y = -4(x + 3)² + 4

d)

y = -4(x - 3)² + 4

36.

Which equation has a vertex of (-3, 4)?

a)

y = 2(x+3)²+ 4

b)

y = (x+3)² - 4

c)

y = (x-3)² + 4

d)

y = 2(x - 3)² + 4

37.

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

Choose the correct graph of the equation.

a)

b)

c)

d)

38.

a)

A

b)

B

c)

C

d)

D

39.

Write the vertex form of the equation that has the indicated vertex and passes through the given point.
Vertex (-2,5); point (0,9)

a)

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

b)

$f\left(x\right)=\left(x-5\right)^2$

c)

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

d)

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

40.

Write the vertex form of the equation that has the indicated vertex and passes through the given point.
Vertex (1,-2); point (-1,14)

a)

$f\left(x\right)=-2\left(x-14\right)^2-1$

b)

$f\left(x\right)=\left(x+14\right)^2$

c)

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

d)

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

41.

Write the vertex form of the equation that has the indicated vertex and passes through the given point.
Vertex (1,-2); point (-1,14)

a)

$f\left(x\right)=-2\left(x-14\right)^2-1$

b)

$f\left(x\right)=\left(x+14\right)^2$

c)

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

d)

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

42.

Solve: x² - 11x + 24 = 0

a)

-3 , -8

b)

3 , 8

c)

4 , 6

d)

12 , -2

43.

Solve: x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

44.

Factor x² + 7x + 12

a)

(x + 2)(x + 10)

b)

(x + 3)(x + 4)

c)

(x + 4)(x + 5)

d)

(x + 4)(x + 6)

45.

What are the factors of x²+3x-40

a)

(x+10)(x-4)

b)

(x+8)(x-5)

c)

(x+20)(x-2)

d)

(x+1)(x-3)

46.

Factor as the product of two binomials.

$x^2+11x+18=$

a)

$\left(x+9\right)^2$

b)

$\left(x+9\right)\left(x+2\right)$

c)

$\left(x+3\right)^2$

d)

$\left(x+2\right)\left(x-2\right)$

47.

Solve using the Zero-Product Property.

(x + 4)(x − 3) = 0

a)

x = 4 and x = −3

b)

x = 2 and x = 1

c)

x = −4 and x = 3

d)

x = −2 and x = 1

48.

What are the solutions to the quadratic equation?

a)

0 and 5

b)

0 and -5

c)

5 and -5

d)

1 and 5

49.

Solve by factoring.
k²+ 8k + 12 = 0

a)

-2, 2

b)

-2, 4

c)

-2, -6

d)

2, 3

50.

Solve for the values of x:
(x + 2)(x - 3) = 0

a)

{ 2, 3 }

b)

{ -2, -3 }

c)

{ 2, 3 }

d)

{ -2, 3 }

51.

Solve and find your zeros:
z(z - 15)=0

a)

z=0 and z=15

b)

z=0 and z=-15

c)

z=-15

d)

z=15

52.

Factor: 49x² - 100

a)

(49x + 100)(x - 1)

b)

(7x - 10)(7x + 10)

c)

(49x - 10)(x + 10)

d)

(7x -10)(7x - 10)

53.

Factor: 3x²- 6x - 24

a)

(3x - 8)(x + 3)

b)

(3x + 4)(x - 6)

c)

3(x - 2)(x + 4)

d)

3(x + 2)(x - 4)

54.

Select the solution(s) for the quadratic: $x^2-11x+19=-5$

a)

3

b)

8

c)

-9

d)

-3

55.

x²=18x-81

a)

x= -9, -9

b)

x= 9, 9

c)

x= -9, 9

56.

$3p^2-17p=30-8p$

a)

$\left\{3,5,-2\right\}$

b)

$\left\{2,-5\right\}$

c)

$\left\{-2,5\right\}$

d)

$\left\{-6,15\right\}$

57.

What are the solutions of the equation $x^2\ =\ -9x$

a)

-9, 3

b)

0, -9

c)

0, 9

d)

1, 9

58.

Solve: $x^2=-3x+4$

a)

$-1,\ 4$

b)

$-4,\ 1$

c)

$\frac{1}{4},\ -1$

d)

$-3,\ 4$

59.

$x^2-100=0$

a)

$\left\{25,4\right\}$

b)

$\left\{-50,2\right\}$

c)

$\left\{-10,10\right\}$

d)

$\left\{0,100\right\}$

60.

Solve.
n² - 2n = 0

a)

n = 2 and 0

b)

n = -2 and 0

c)

n = 2

d)

n = 0

61.

Factor

$x^2-17x+60$

a)

(x + 30)(x - 2)

b)

(x - 12)(x - 5)

c)

(x + 10)(x - 6)

d)

(x - 4)(x + 15)

62.

$\left(c+6\right)\left(c-7\right)=0$

a)

$c=-6,\ c=7$

b)

$c=6,\ c=-7$

c)

$c=6,\ c=7$

d)

$c=-6,\ c=-7$

63.

Solve
x² + 13x + 12 = 0

a)

x = -12, -1

b)

x = 12, 1

c)

x = 13, 1

d)

x = -13, -1

64.

Which of the following is a factor of:

6x²-5x - 4

a)

(3x - 4)

b)

(2x - 1)

c)

(3x + 4)

d)

(2x - 3)

65.

Factor:
2n² + 3n - 9

a)

(2n - 9)(n + 1)

b)

2n + 3)(n + 3)

c)

(2n + 3)(n - 3)

d)

(2n - 3)(n + 3)

66.

Factor Completely: 6x² + 7x - 3

a)

(2x + 3)(3x-1)

b)

(2x - 3)(3x + 1)

c)

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

d)

(3x - 3)(2x + 1)

67.

Factor Completely: 4x² - 20x + 25

a)

(4x - 25) (x -1)

b)

(2x + 5) (2x - 5)

c)

(2x - 5)²

d)

(4x - 5) (x - 5)

68.

Factor Completely: 9x² - 49

a)

(3x + 7)(3x + 7)

b)

(3x + 7)(3x - 7)

c)

(3x - 7)(3x - 7)

d)

Not factorable

69.

What are the solutions?

(x-5)(x+6)=0

a)

{5,5 }

b)

{ -5,-5 }

c)

{ -5,-6 }

d)

{5,-6 }

70.

$y=4(x+2)^2-8$

Convert the equation from vertex form to standard form.

a)

$y=4x^2+16x+8$

b)

$y=4x^2+16x+16$

c)

$y=16x^2+64x-8$

d)

$y=16x^2+256x+8$

71.

a)

A

b)

B

c)

C

d)

D

72.

a)

A

b)

B

c)

C

d)

D

73.

a)

A

b)

B

c)

C

d)

D

74.

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

75.

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

76.

Convert to vertex form.

a)

y=-(x-5)² + 21

b)

y=-(x+5)² + 21

c)

y=-(x+10)² + 21

d)

y=-(x-10)² + 21

77.

Convert to vertex form.

a)

y=2(x+3)² - 9

b)

y=2(x-3)² - 9

c)

y=2(x+6)² - 9

d)

y=2(x-6)² - 9

78.

Which of the following represents the first step in solving:

y = x² + 3x - 5

y = x + 3

a)

x² - 3x + 5 = x - 3

b)

x² + 3x - 5 = x + 3

c)

x² + 3x - 5 + x + 3 = 0

d)

x² + 3x - 5 = 0

79.

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)

80.

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)

81.

Determine the solution to the given linear-quadratic function.

a)

(0, 0)

b)

(3, 0)

c)

(2, -3)

d)

(-3, 2)

82.

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

a)

0 solutions

b)

1 solution

c)

2 solutions

d)

3 solutions

83.

Which of the following graphs correctly represents:

y=x²

y=-2x+1

a)

b)

c)

d)

84.

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)

85.

a)

A

b)

B

c)

C

d)

D

86.

What are the solutions to this quadratic/ linear system?

a)

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

b)

No Solutions

c)

-6 and -10

d)

(1,-6)

87.

Determine the number of solutions to this system of equations.

a)

No solution

b)

1 solution

c)

2 solutions

d)

infinite solutions

88.

Determine the number of solutions to this system of equations.

a)

No solution

b)

1 solution

c)

2 solutions

d)

infinite solutions

89.

Find the solution(s).

$y=x^2-24$

$y=x-12$

a)

(2,3) and (3,-15)

b)

(-3,-15) and (4,-8)

c)

(-3,15) and (8,4)

d)

(-8,4) and (-4,10)

90.

Find the solution(s).

a)

(3,18) and (-4, 15)

b)

(5,2) and (5,-9)

c)

(-4,-4)

d)

(-4,2)

91.

Solve for a by factoring.

a² + 2a - 24 = 0

a)

a = -6 and a = 4

b)

a = 6 and a = -4

c)

a = 12 and a = -2

d)

a = 8 and a = -3

92.

Solve the equation $2a^2-3a=9$ algebracially.

a)

$a=-\frac{2}{3},\ 1$

b)

$a=\frac{2}{3},\ -1$

c)

$a=-\frac{3}{2},\ 3$

d)

$a=\frac{3}{2},\ -3$

93.

Solve the equation $2x^2-15=7x$ algebracially.

a)

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

b)

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

c)

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

d)

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

94.

What are the x-intercepts

y=-(x–1)(x+4)

a)

(0,4) (0,-1)

b)

(-4,0) (1,0)

c)

(0,-4) (0,1)

d)

(-1,0) (4,0)

95.

What are the x-intercepts

y=(x–1)(x–3)

a)

(0,3) (0,1)

b)

(1,0) (3,0)

c)

(0,-3) (0,-1)

d)

(-1,0) (-3,0)

96.

Which of the following is the graph of y = –3(x – 7)(x – 5)?

a)

b)

c)

d)

97.

Write the equation for the quadratic function shown in the graph.

a)

y = 3 (x – 1)(x – 3)

b)

y = –3 (x – 1)(x – 3)

c)

y = 3 (x + 1)(x + 3)

d)

y = 3 (x + 1)(x – 3)

98.

What is the equation of this graph in intercept form?

a)

y = 2(x + 3)(x - 1)

b)

y = 2(x - 3)(x + 1)

c)

y = -2(x - 3)(x + 1)

d)

y = -2(x + 3)(x - 1)

99.

Which quadratic equation models the parabola shown?

a)

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

b)

y = (x + 2)(x + 5)

c)

y = -(x - 2)(x - 5)

d)

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

100.

What are the x-intercepts for the function below?

y=\left(x-3\right)\left(x+7\right)

a)

(3, 0) and (7, 0)

b)

(3, 0) and (-7, 0)

c)

(-3, 0) and (7, 0)

d)

(-3, 0) and (-7, 0)

Alg2H Unit 2 Test Practice

Total questions: 100

Worksheet time: 10hrs 46mins

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