Free Printable Unit 6: Quadratics & Applications Final Exam Review Sem 2

1.

Does this parabola have a maximum or minimum?
REMEMBER MAXIMUM IS THE HIGHEST AND MINIMUM IS THE LOWEST.

a)

Maximum

b)

Minimum

2.

If the a value is negative, which direction does the parabola open?

a)

up

b)

down

c)

left

d)

right

3.

Which answer choice describes y = -3x² +7x - 2 accurately?

a)

opens up with a maximum

b)

opens up with a minimum

c)

opens down with a maximum

d)

opens down with a minimum

4.

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

a)

16

b)

8

c)

-8

d)

-24

5.

Does this graph have a maximum or minimum?

a)

Minimum

b)

Maximum

6.

What is the green dot on the parabola called?

a)

maximum

b)

minumum

c)

roots

d)

zeros

7.

Is this a max or min?

a)

max

b)

min

c)

cannot be determined

8.

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

9.

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

10.

Does this parabola have a minimum or maximum and what is its value?

a)

minimum: 2

b)

maximum: 2

c)

minimum: 5

d)

maximum: 5

11.

Which transformation maps the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

a)

a reflection across the line x = -4

b)

a reflection across the line y = -4

c)

a translation shifting f(x) 4 units to the left

d)

a translation shifting f(x) 4 units to the right

12.

Pablo throws a ball with a path of
h = -5(t - 2)².
Maria throws a ball with a path of
h = -5(t - 2)² + 10.
Which description is reasonable for the difference in the two equations?

a)

Maria throws the ball 10 times harder than Pablo does.

b)

Maria starts her ball at a height 10 feet higher than Pablo does.

c)

Pablo throws the ball 10 times harder than Maria does.

d)

Pablo starts his ball at a height 10 feet higher than Maria does.

13.

Match the description to its equation.
Reflected over the x-axis
Stretched by a factor of 2

a)

A

b)

B

c)

C

d)

D

14.

Match the description to its equation.
Moves up 2
Moves left 4

a)

A

b)

B

c)

C

d)

D

15.

Match the description to its equation.
Moves right 7

a)

A

b)

B

c)

C

d)

D

16.

Match the description to its equation.
- moves down 3

a)

A

b)

B

c)

C

d)

D

17.

Which list orders the quadratic functions from narrowest to widest?

a)

y = x²
y = 4x²
y = 2x² - 2
y = 0.5 x²

b)

y = 0.5 x²
y = x²
y = 2x²- 2
y = 4x²

c)

y = 4x²
y = 2x²- 2
y = x²
y = 0.5 x²

d)

y = 2x² - 2
y = 4x²
y = 0.5x²
y = x²

18.

Find the y-intercept of the quadratic function

a)

A

b)

B

c)

C

d)

D

19.

Find the y-intercept of the quadratic function

a)

A

b)

B

c)

C

d)

D

20.

(x-2)(3x+1) what are the solutions to this equation?

a)

x=2 and -1

b)

x= -2 and 1

c)

x= 2 and -3

d)

x=2 and -1/3

21.

Factor:
x² + 5x - 24

a)

(x - 8)(x + 3)

b)

(x + 8)(x - 3)

c)

(x + 6)(x - 4)

d)

(x + 12)(x - 2)

22.

Find the solutions of the factored equation: x(x+3) = 0

a)

x=0 and x=-3

b)

x=0 and x=3

c)

x=-3 and x=3

d)

No solutions

23.

What are the solutions when factoring?

a)

x = 6,2

b)

x = -6, -2

c)

x = 8, 12

d)

x = 4, 4

24.

The solutions of the quadratic equation

x²+2x-15=0 are (hint: find the zeros) FACTOR

a)

x = 3 or x = 5

b)

x = 5 or x = -3

c)

x = -5 or x = 3

d)

x = -3 or x = -5

25.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

26.

What are the factors of (4x² - 14x - 8)?

a)

(4x - 8)(x + 1)

b)

(4x + 8)(x - 1)

c)

(4x + 2)(x - 4)

d)

(2x - 1)(2x + 8)

27.

Solve
2x² + 17x + 21 = 0

a)

x= ^-21/₂, -17

b)

x= ²/₃, 16

c)

x=-7, ^-3/₂

d)

x=15, -³/₇

28.

Which are solutions for the equation? $x^2=16$

a)

x = 4

b)

x = -4

c)

x = 8

d)

x = 16

e)

x = -2

29.

Which are solutions for the equation? $x^2=100$

a)

x = 10

b)

x = -10

c)

x = 25

d)

x = 50

e)

x = -25

30.

Which are solutions for the equation? $x^2-1=8$

a)

x = 3

b)

x = -3

c)

x = 4

d)

x = -4

e)

x = 9

31.

Which are solutions for the equation? $x^2=0$

a)

x = 0

b)

x = -3

c)

x = 10

d)

x = -4

e)

x = 9

32.

Which are solutions for the equation? $2x^2=18$

a)

x = 3

b)

x = -3

c)

x = 2

d)

x = -2

e)

x = 9

33.

Which are solutions for the equation? $3x^2=75$

a)

x = 5

b)

x = -5

c)

x = 15

d)

x = -25

e)

x = 25

34.

Which are solutions for the equation? $\left(x-3\right)\left(x-3\right)=0$

a)

x = 3

b)

x = -3

c)

x = 9

d)

x = -9

e)

x = 0

35.

Which are solutions for the equation? $\left(x-7\right)\left(x+3\right)=0$

a)

x = -3

b)

x = 7

c)

x = 10

d)

x = -10

e)

x = -21

36.

Which are solutions for the equation? $x\left(x-8\right)=0$

a)

x = 8

b)

x = 0

c)

x = -8

d)

x = 7

e)

x = -16

37.

Which are solutions for the equation? $\left(x-1\right)\left(x-1\right)=16$

a)

x = -3

b)

x = 5

c)

x = -5

d)

x = 3

e)

x = -16

38.

Which are solutions for the equation? $\left(x-1\right)\left(x-1\right)=25$

a)

x = -4

b)

x = 6

c)

x = -6

d)

x = 4

e)

x = -25

39.

Which are solutions for the equation? $\left(x+1\right)\left(x+1\right)=9$

a)

x = -4

b)

x = 2

c)

x = -2

d)

x = 4

e)

x = -9

40.

Which are solutions for the equation? $\left(x+1\right)^2=9$

a)

x = -4

b)

x = 2

c)

x = -2

d)

x = 4

e)

x = -9

41.

Which are solutions for the equation? $\left(x+1\right)^2=144$

a)

x = -13

b)

x = 11

c)

x = -11

d)

x = 13

e)

x = 72

42.

Which are solutions for the equation? $x^2+7=107$

a)

x = -10

b)

x = 10

c)

x = -11

d)

x = 11

e)

x = 100

43.

x-intercepts are also called:

Choose ALL that apply!

a)

Solutions

b)

Roots

c)

Zeros

d)

Parabolas

e)

Puppies

44.

$x=\frac{-\left(b\right)\sqrt{\left(a\right)^2-4ac}}{2b}$ What is wrong with this formula? Check ALL that apply.

a)

Missing $\pm$ after $-\left(b\right)$

b)

The square root should be $\sqrt{\left(b\right)^2-4ac}$

c)

The denominator should be $2a$

d)

There are no errors. It is correct.

45.

Choose the correct values for a, b, and c.

$4x^2-5x\ =\ 9$

a)

a = 4

b)

b = 5

c)

c = 9

d)

b = -5

e)

c = -9

46.

$x^2-4x-7=0$ Which example below uses the quadratic formula correctly?

a)

$x=\frac{-\left(4\right)\pm\sqrt{\left(-4\right)^2-4\left(1\right)\left(-7\right)}}{2\left(1\right)}$

b)

$x=\frac{-\left(-4\right)\pm\sqrt{\left(-4\right)^2-4\left(1\right)\left(-7\right)}}{2\left(1\right)}$

c)

$x=\frac{-\left(-4\right)\pm\sqrt{\left(-4\right)^2-4\left(1\right)\left(7\right)}}{2\left(1\right)}$

47.

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

AXIS OF SYMMETRY:

$-\frac{B}{2A}$

a)

x = -4

b)

x = 4

c)

y = 4

d)

y = -4

48.

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

HINT: AXIS OF SYMMETRY:

$-\frac{B}{2A}$

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

49.

What are the zeros of

$f\left(x\right)=x^2+7x-18$ ?

QUADRATIC FORMULA:

$\frac{-b\pm\sqrt[]{b^{2\ }-4ac}}{2a}$

a)

$x=-2,\ -9$

b)

$x=2,\ -9$

c)

$x=-2,\ 9$

d)

$x=2,\ 9$

50.

How many solutions can a quadratic have?

a)

1 solution

b)

3 solutions

c)

0 solutions

d)

2 solutions

51.

Solve the equation by factoring.

a)

x = {-5,-3}

b)

x = {5,-3}

c)

x = {-5,3}

d)

x = {5,3}

52.

Solve the equation by factoring.

a)

x = {1}

b)

x = {-1}

c)

x = { }

d)

no solution

53.

Solve the equation by factoring.

a)

x = {3,8}

b)

x = {-3,8}

c)

x = {3,-8}

d)

x = {-3,-8}

54.

What is the quadratic formula?

a)

b)

c)

d)

55.

Solve the equation using the quadratic formula.

x² + 7x = x - 10

a)

-6/2 + √4

b)

-6/2 - √4

c)

no solution

d)

∅

56.

Solve the equation using the quadratic formula.

4x² +9x = 12x

a)

x = {0, 3/4}

b)

x = {0, -3/4}

c)

x = {0, 4/3}

d)

no solution

57.

Use the discriminant to find the number of solutions for the following equation.

y = x² +10x + 25

a)

2 solutions

b)

1 solution

c)

0 solutions

58.

Use the discriminant to find the number of solutions for the following equation.

y = -3x²+5x - 8

a)

2 solutions

b)

1 solution

c)

0 solutions

59.

Use the discriminant to find the number of solutions for the following equation.

y = 4x² - 9

a)

2 solutions

b)

1 solution

c)

0 solutions

60.

Which value is the y-intercept?

a)

(-4, 0)

b)

(-1, -9)

c)

(0, -8)

d)

(2, 0)

61.

What are the zeros of this graph?

a)

x = {-4, 2}

b)

(-4, 0 ) and (2, 0)

c)

x = {-1, 0}

d)

(-1, 9 ) and (0, -8)

62.

What is the equation for standard form?

a)

y = x²+ bx + c

b)

y = ax²+ bx + c

c)

y = mx + b

d)

Ax + By = C

63.

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)

64.

A fountain shoots water in an arc over a lake that can be modeled by the graph of the equation y= -0.4x² + 8x where x is the horizontal distance (in feet) from the fountain base and y is the height (in feet) above the river. How high does the water go?

a)

It goes 11.78 feet high

b)

It goes 20 feet high

c)

It goes 40 feet high

d)

It goes 10 feet high

65.

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?

a)

-4

b)

2

c)

4

d)

8

66.

What is the initial (starting) height of an object following this path? h(t) = -16t² +20t + 6

a)

-16 feet

b)

0 feet

c)

20 feet

d)

6 feet

67.

If the graph shows price vs profit, what is the maximum profit?

a)

35

b)

12,000

c)

12,500

d)

60

68.

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

69.

A lizard is jumping across the water in search of food. The equation h = -12t² + 6t models the lizard's height in feet above the water t seconds after he jumps. How long after jumping is he back on the water?

a)

0.1 seconds

b)

0.25 seconds

c)

0.50 seconds

d)

0.75 seconds

e)

1 second

70.

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

a)

Set the equation = 0 and solve.

b)

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

c)

Substitute x = 0 into the equation.

d)

Find the y-coordinate for the vertex.

71.

If I want to find out when an object hits the ground, I should _________.

a)

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

b)

Set my equation = 0 and solve.

c)

Replace x with 0 and evaluate.

d)

Find the y-coordinate of the vertex.

72.

If I want to see the initial height of an object, I should _____________.

a)

Substitute x = 0 into the equation and evaluate.

b)

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

c)

Find the y-coordinate of the vertex.

d)

Set my equation = 0 and solve.

73.

How long is the rocket in the air?

a)

8 seconds

b)

4 seconds

c)

6 seconds

d)

260 seconds

74.

What is the greatest height the rocket reaches?

a)

250 feet

b)

240 feet

c)

260 feet

d)

260 seconds

75.

About how high is the rocket after 1 second?

a)

50 feet

b)

100 feet

c)

190 feet

d)

1 foot

76.

About how high is the rocket after 2 seconds?

a)

50 feet

b)

100 feet

c)

190 feet

d)

200 feet

77.

At 2 seconds is the rocket going up or down?

a)

up

b)

down

78.

About how high is the rocket after 6 seconds?

a)

50 feet

b)

100 feet

c)

190 feet

d)

1 foot

79.

At 6 seconds is the rocket going up or down?

a)

up

b)

down

80.

Is the rocket traveling faster between 0-1 second or between 3-4 seconds?

a)

0-1 second

b)

3-4 seconds

81.

Use the equation to find the EXACT value of the height of the rocket at 2 seconds. $h\left(t\right)=-16t^2+128t$

a)

191 feet

b)

192 feet

c)

193 feet

d)

194 feet

82.

This graph represents a DIFFERENT rocket. Use the equation to find the MAXIMUM height of this rocket $f\left(x\right)=-16x^2+80x$

a)

200 feet

b)

100 feet

c)

150 feet

d)

50 feet

Unit 6: Quadratics & Applications Final Exam Review Sem 2

Total questions: 82

Worksheet time: 3hrs 48mins

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