1 The width of a rectangle is 4 feet more than its length.
The area is 117 feet. What is the length of the rectangle, to the nearest tenth?
2 The table below shows values for the function f (x) = x2 + 2x - 8.
x
f(x)
-4
-2
-8
0
-8
6
40
2
4
What is the solution set for f(x) = 0?
0
0
16
3 The area of a rectangle is 54 square meters.
The length is (2x) and the width is (4x – 3). Find x
and give the length and width:
4 The function h = – 16t2 +96t + 20 represents h, the height of a ball thrown into the air,
for t seconds with an initial velocity of 96 feet per second from an initial height of 20 feet.
What would be the maximum height?
5 The graph of an equation is shown below.
A. List the x-intercepts of the graph.
B. What are the solutions of the equation?
C. Write an equation that represents the solutions.
6 What is the solution set for the quadratic equation y = (x - 6)2 – 9?
7 Given the parent function y = x2 .
A. What is the equation of the graph when it is shifted 4 units
down?
B. In the grid below, draw the graph of the parent function and
the graph from part A.
C. Explain the change from points on the graph of y = x2 if the graph were translated to
y = x2 – 10.
8 These equations are graphed on a coordinate graph.
Equation 1: y =
x2
Equation 2: y = x2 +
3
How does the graph of Equation 1 differ from the graph of Equation 2?
9 Given the parent function y = x2.
A. If the y-coordinates of the graph of the function were increased by a factor of 5, what
would be the new function?
B. If the y-coordinates of the graph were increased by a factor of ¼, what would be the new
function?
C. Sketch all three graphs below:
10 In the grid below, draw the graph of the equation y = –2x2 + 2.
11 A rock is dropped off the top of a building 140 feet tall so that its height above the
ground is modeled by h = -16t2 + 92t + 140 .
What is a reasonable domain for the time during which the ball is in the air?
12 The area of a square is A = s2. A square lot is to be used for the construction of a
building that is to have a square foundation.
If the building must have a square footage of no less than 900 sq. feet and no more than
5,625 sq. ft, the domain of the area function must be which of the following?
13 Explain how EACH formula does or does not represent the entire area of the shape
below: (2 are correct, 2 are wrong)
13a.) Area = a(a + b)
13b.) Area = a2 + b2
13c.) Area = a2 + b
13d.) Area = a2 + ab
14 The distance, d, that an object has fallen in t seconds after being dropped is negative
5 times the square of the time that the object is in the air. Write an expression for
distance as a function of time:
15 This scatter plot represents the acceleration of an amusement park ride with velocity
shown as a function of time.
A.) After how many seconds would the ride reach 25 miles per
hour?
B.) What is the maximum speed of the ride and how long does
it take to reach that speed?
16 A certain function is represented by f(x) = -2x2 - x + 5.
16a.) What is the value of f (-4)?
16b.) What is the value of f(4)?
16c.) What is x when f(x) = 2?
17 A box has a length which is represented by (x+2) units, a width which is (2x+1) units,
and a height of 4 units.
Write the equation that would be used to find x if the volume of the box is 108 cubic units.
18 The owner of a resale shop calculates that his profit is x2 - 14x + 485, where x is the
number of items sold.
How many items must he sell in order for his profit to be $1012?
19 This graph shows the distance, d, in feet that an object falls in t seconds.
Based on this graph, how many feet does an object fall between
2 seconds and 4 seconds?
20 The equation below represents h, the height of a ball thrown upward, and the time, t, it
takes to hit the ground.
h = 50t - t 2
A. What is the height of the ball after three seconds?
B. In the table below, complete the heights for the given seconds.
Time
(sec.)
1
2
3
4
5
6
Height
(feet)
C. In the grid below, draw the graph of the equation h = 50t - t 2 .
D. What is the amount of time it took for the ball to hit the ground?
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