Free Printable Unit 4A Final Review & Retest Remediation

1.

Which rule represents the Quadratic relationship of the square tiles?

a)

$n^2+1$

b)

$2n^2+1$

c)

$n^2+3$

d)

$\left(n+1\right)^2$

2.

How many square tiles will be in the 10th stage of this pattern?

(a)

3.

Does this graph have a maximum or minimum value?

a)

maximum

b)

minimum

c)

neither

d)

both

4.

What is the vertex?

a)

(2, 4)

b)

(3, -1)

c)

(0, 8)

d)

(4, 2)

5.

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

a)

(6 , 0)

b)

(-6 , 0)

c)

(0, -6)

d)

(0 , 6)

6.

What is the green dashed line called?

a)

roots or x-intercepts

b)

parabola

c)

axis of symmetry

d)

line of dashes

7.

What is the axis of symmetry?

a)

x = - 4

b)

x = - 2

c)

x = 0

d)

x = 4

8.

What is the range?

a)

$\left(-\infty,4\right]$

b)

$\left(-\infty,-2\right]$

c)

All Real Numbers

d)

$\left[4,\ \infty\right)$

9.

What is the y-intercept?

a)

(3,0)

b)

(0,-3)

c)

(0,3)

d)

(-3,0)

10.

What is the range of this function?

a)

$\left[-\infty,-4\right)$

b)

$\left[1,\infty\right)$

c)

All Real Numbers

d)

$\left[-4,\infty\right)$

11.

What is the domain of the function?

a)

All Real Numbers

b)

$\left[-\infty,4\right)$

c)

$\left[-1,\infty\right)$

d)

$\left(-3,-1\right)$

12.

Where is this graph positive?

a)

(-3, 1)

b)

All real numbers

c)

$\left(1,\ \infty\right)$

d)

$\left(-\infty,\ -3\right)$

13.

Where is this graph negative?

a)

(-3, 1)

b)

All real numbers

c)

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

d)

$\left(-\infty,\ -3\right)$

14.

Determine the interval in which this function is INCREASING.

a)

(-4, ∞)

b)

(-3, ∞)

c)

(∞, -3)

d)

(-∞, -4)

15.

Determine the interval in which this function is DECREASING.

a)

(-3, ∞)

b)

(-3, ∞)

c)

(-∞, -4)

d)

(-∞, -3)

16.

Describe the end behavior of the graph.

a)

x → ∞, y→ ∞ and
x→ ∞, y→⁻∞

b)

x → ∞, y→ ∞ and
x→⁻∞, y→∞

c)

None of these

d)

x →∞,y→⁻∞ and
x→∞, y→⁻∞

17.

Which of the following is an interval where the function is negative?

a)

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

b)

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

c)

$\left(-\infty,0\right)$

d)

$\left(-4,\ 0\right)$

18.

What are the roots of the following quadratic? (Hint: roots is another work for x-intercepts.)

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

19.

Which of the following statements is true?

a)

The interval of increase is $\left(-\infty,\ -1\right]$

b)

The axis of symmetry is x = 4

c)

The range is $\left[4,\ \infty\right)$

d)

The interval of decrease is $\left(4,\ \infty\right)$

20.

Which of the following statements is true?

a)

The range is $\left[0,\ \infty\right)$

b)

The graph is increasing on $\left(4,\ \infty\right)$

c)

The graph is positive on $\left(-\infty,\ 0\right)$

d)

The y-intercept is (0, 4)

21.

What are the x-intercepts of the function $y\ =\ \left(x-3\right)\left(x\ +\ 4\right)$

a)

(3, 0) and (-4, 0)

b)

(-3, 0) and (4, 0)

c)

(0, 3) and (0, -4)

d)

(-3, 4) and (0, 0)

22.

What is the y-intercept of the function $y\ =\ -2x^2+3x\ -\ 5$

a)

(0, -2)

b)

(-5, 0)

c)

(0, -5)

d)

(0, 3)

23.

What is the vertex for the function $y\ =\ 2\left(x-1\right)^{2\ }+\ 3$

a)

(1, 3)

b)

(-1, 3)

c)

(2, 3)

d)

(2, 1)

24.

What is the vertex for the function $y\ =\ 2x^{2\ }-\ 8x\ +\ 3$

a)

(2, -5)

b)

(-5, 2)

c)

(2, 5)

d)

(-2, 27)

25.

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

26.

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

27.

Amelia runs a catering business. Based on her records, her profit is shown by P = 2x² - 44x -150, where x is the number of meals she caters and P is her profit. When P is negative, Amelia loses money. What is the least number of meals Amelia needs to cater in order to begin making profit?

a)

-1

b)

5

c)

11

d)

25

e)

50

28.

You and some friends went to a haunted house on Halloween. The mummy scared one friend so much that she jumped into the air! The equation h = -4t² + 2t models her jump where h is her jump's height in feet t seconds after the mummy scares her. How long was she in the air?

a)

0.1 seconds

b)

0.25 seconds

c)

0.50 seconds

d)

1 second

e)

2 seconds

29.

If the graph shows price vs profit, at which prices would you "break even" (neither lose or gain money)?

a)

10 and 60

b)

20 and 50

c)

30 and 40

d)

35

30.

A rock is dropped from a bridge 320 ft. above a river. The pathway that the rock takes can be modeled by the equation h = -16t² + 320. How long will it take for the rock to reach the river (i.e. hit the "ground")?

a)

2.5 sec

b)

3.5 sec

c)

4.5 sec

d)

3.8 sec

31.

The function f(t) = -5t²+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

a)

4 seconds

b)

-2 seconds

c)

-6 seconds

d)

9 seconds

32.

A rectangle has an area of 24 square units. The width is 5 units less than the length. What is the length, in units, of the rectangle?

a)

6

b)

8

c)

3

d)

19

33.

Which of the following expressions represents the pattern?

a)

n

b)

n + 2

c)

n²

d)

n² + 2

34.

How many dots would be in the 6th step in the sequence?

a)

9

b)

11

c)

13

d)

36

35.

Which of the following expressions represents the pattern?

a)

n

b)

n + 2

c)

n²

d)

n² + 2

36.

How many blocks would be in the 7th step in the sequence?

a)

51

b)

11

c)

13

d)

36

37.

Dorothy loves to make cakes. The following table shows how the number of eggs that she has left changes as she makes cakes.
What is the meaning of the y-intercept?

a)

She uses 5 eggs for every 2 cakes.

b)

She started with 47 eggs.

c)

She uses 47 eggs for every 0 cakes.

d)

She started with 5 eggs.

38.

Identify the transformation from the graph of f(x)=2^xto the graph g(x)=2^x-3

a)

shifted up three units

b)

shifted down three units

c)

shifted left three units

d)

shifted right four units

39.

What are the following transformations:
-f(x) - 4

a)

reflection over the x axis and 4 units right

b)

reflection over the x axis and 4 units down

c)

reflection over the y axis and 4 units right

d)

reflection over the y axis and 4 units down

40.

Which student represents a Quadratic Function?

a)

Beth

b)

Maria

c)

Tracy

d)

None of the above

41.

Which statement is true based on the data in the table?

a)

f(x) is a quadratic function

b)

g(x) is a linear function

c)

The y-intercept of g(x) is 8

d)

The slope of f(x) is 3

42.

What function is represented by the table?

a)

Exponential

b)

Linear

c)

Quadratic

43.

What kind of function is represented by this table?

a)

Exponential

b)

Linear

c)

Quadratic

44.

All Quadratic Functions have a ________________

a)

Common Ratio

b)

Common 1st Difference

c)

Common 2nd Difference

d)

None of these

45.

Pick a function that best models the following situation: A speed of a rollercoaster from start to finish.

a)

Exponential

b)

Linear

c)

Quadratic

d)

Neither

46.

What is the average rate of change from x=0 to x=1

a)

-3

b)

3

c)

0

d)

2

47.

Average Rate of Change is also known as...

a)

y-intercept

b)

x-intercept

c)

linear

d)

slope

48.

Determine the interval in which this function is DECREASING.

a)

(-3, ∞)

b)

(-3, ∞)

c)

(-∞, -4)

d)

(-∞, -3)

49.

Determine the interval of this function's DOMAIN.

a)

(-5, -1)

b)

(-∞, ∞)

c)

No solution

d)

(-∞, -3)

50.

The function is INCREASING if as the x-values increase the y-values _______________.

a)

Increase

b)

Decrease

c)

Stay the Same

d)

Double in value

51.

The function is DECREASING if as the x-values increase the y-values _______________.

a)

Increase

b)

Decrease

c)

Stay the Same

d)

Double in value

52.

Identify where the function is negative.

a)

$x<-3,\ \ \ x\ >3$

b)

$-3<x<3$

c)

All Real Numbers

53.

Describe the end behavior of the graph.

a)

x → +∞, y→ +∞ and

x→ +∞, y→⁻∞

b)

x → +∞, y→ +∞ and

x→⁻∞, y→+∞

c)

None of these

d)

x →+∞,y→⁻∞ and

x→+∞, y→⁻∞

54.

Describe the end behavior of the graph.

a)

x →∞, y→⁻∞ and x →⁻∞,y→⁻∞

b)

x →∞, y→∞ and x→⁻∞, y→∞

c)

x →∞, y→∞ and x→⁻∞, y→0

d)

x →∞,y→∞ and x→⁻∞, y→⁻∞

55.

What is the name of this form:
y = ax² + bx + c

a)

vertex form

b)

standard form

c)

factored form

d)

zero form

56.

Does the equation open up or down?
Y = -3x² +7x - 2

a)

up

b)

down

c)

Neither; it opens to the right.

d)

Neither; it opens to the left.

57.

What is Mrs. Gordon's rate from 0 to 2 seconds?

a)

2.5 feet per second

b)

.4 feet per second

c)

5 feet per second

d)

.2 feet per second

58.

Calculate the average rate of change from 20 to 40 minutes.

a)

-2 minutes per gallon

b)

-20 minutes per gallon

c)

-2 gallons per minute

d)

-20 gallons per minute

59.

What key feature helps you find the initial height?

a)

x-intercept

b)

y-intercept

c)

x value of vertex

d)

y vertex of vertex

60.

What key feature helps you find how long the object is in the air/when the object hits the ground?

a)

x-intercept

b)

y-intercept

c)

x value of vertex

d)

y value of vertex

61.

What key feature helps you find the maximum height?

a)

x-intercept

b)

y-intercept

c)

x value of vertex

d)

y value of vertex

62.

What key feature helps you find when the object reaches its maximum height?

a)

x-intercept

b)

y-intercept

c)

x value of vertex

d)

y vertex of vertex

63.

Which of the following best describes the vertex of a quadratic function in the context of a real-world situation?

a)

The maximum or minimum point of the parabola

b)

The y-intercept of the function

c)

The point where the parabola crosses the x-axis

d)

The rate of change of the function

64.

In the quadratic function $f(x)=ax^2+bx+c$ , what does the coefficient 'a' determine?

a)

The y-intercept of the parabola

b)

The x-intercept of the parabola

c)

Vertical Stretch or Compression and/or reflection over x-axis

d)

The axis of symmetry of the parabola

65.

A ball is launched at 20 m/sec from a 50 m tall platform. The function of the ball’s height (h) at time (t) seconds after launch is $h(t)=-5t^2+20t+50$ . What is the domain of this situation?

a)

all real numbers

b)

all real numbers less than zero

c)

all real numbers less than or equal to zero

d)

all real numbers greater than or equal to 1

e)

all real numbers greater than or equal to zero

66.

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

Unit 4A Final Review & Retest Remediation

Total questions: 66

Worksheet time: 3hrs 6mins

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