Name: ________________________ Class: ___________________ Date: __________
ID: Pre-AP
REVIEW for Unit 9 Test #1 - Solve Quadratics by Graphing and Finding Square Roots
____
____
1 How would you change the graph of y = x 2 to produce the graph of y = x 2 − 4?
A
shift the graph of y = x 2 left 4 units
B
shift the graph of y = x 2 down 4 units
C
shift the graph of y = x 2 right 4 units
D
shift the graph of y = x 2 up 4 units
3
2 Predict how the graph of the equation y = − x 2 will compare with the graph of the equation y = x 2 .
2
F
G
H
J
____
The graph will open down and will be narrower.
The graph will open up and will be narrower.
The graph will open down and will be wider.
The graph will open up and will be wider.
3 How would you translate the graph of y = x 2 to produce the graph of y = x 2 + 2?
A
translate the graph of y = x 2 down 2 units
B
translate the graph of y = x 2 up 2 units
C
translate the graph of y = x 2 left 2 units
D
translate the graph of y = x 2 right 2 units
4 Answer the following questions about the function shown. Use a calculator if needed.
Where is the vertex of f(x) = −x 2 + 3x + 10?
What is the equation for the line of symmetry?
Is it a maxumum or minimum?
What are the roots of the function?
1
Name: ________________________
ID: Pre-AP
5 A rocket leaves the barrel of a launcher at a height of 5 feet off the floor, with an initial velocity of 160 feet
per second. The equation describing the rocket's height after t seconds is h = −16t 2 + 160t + 5. The graph
below shows the rocket's height as a function of time.
What is the maximum height reached by the rocket and how many seconds did it take for the rocket to reach
that height? Estimate the height value to the nearest 25 feet and the time value to the nearest tenth of a
second.
____
A 200 feet at 2.0 seconds
C 350 feet at 4.0 seconds
B 225 feet at 2.5 seconds
D 400 feet at 5.0 seconds
6 A rocket is launched from atop a 45 foot cliff with an initial vertical velocity of 137 feet per second. The
height of the rocket t seconds after launch is given by the equation h = −16t 2 + 137t + 45. Graph the
equation to find out how long after the rocket is launched it will hit the ground. Estimate your answer to the
nearest tenth of a second.
F
0.3 seconds
G
8.9 seconds
H
1.4 seconds
J
8.2 seconds
7 Find the roots of x 2 + 7x + 41 = −4x + 13 by graphing.
8 Find the zeros of f (x) = 3x 2 − 5x + 7 by graphing.
9 Find the solutions of y = x 2 + 12x + 36 by graphing.
____
10 Tell whether the equation has two solutions, one solution, or no solution. 4x 2 − 7x + 11 = 0
F
two solutions
G
no solution
H
2
one solution
Name: ________________________
____
11 Determine the number of solutions of the equation: −x 2 − 6x − 9 = 0
A
____
ID: Pre-AP
3
B
0
C
1
D
2
12 The number of new cars purchased in a city can be modeled by the equation C = 27t 2 + 214t + 8766, where
C is the number of new cars and t is the number of years since 1974. In what year will the number of new
cars reach 18,000?
F
2000
G
2039
H
1993
1989
J
For #13-20, solve the equation. Round the solutions to the nearest hundredth.
13 x 2 = 121
14
____
1 2
x = 54
6
15 49x 2 − 36 = 0
A
6 6
− ,
7 7
B
7 7
− ,
6 6
C
−
49 49
,
36 36
D
−
36 36
,
49 49
16 5x 2 − 22 = −22
17 5x 2 + 30 = −2x 2 + 9
18
3
2
(n + 1) = 33
2
ÊÁ w − 7 ˆ˜ 2
˜˜ − 20 = 101
19 11ÁÁÁÁ
˜˜
2
Ë
¯
2
20 2 (x + 4) = 86
21 An object is dropped from an initial height of s feet. The object's height at any time t, in seconds, is given by
h = −16t 2 + s. How long does it take for an object dropped from 225 feet to hit the ground? Round your
result to two decimal places.
F
3.75 seconds
G
4.59 seconds
H
3
5.30 seconds
J
6.24 seconds