Algebra II Practice Test Quadratic Functions
Name________________________________________________
Review:
1.
Find ( f o g )( x ) if ( )

2 x

5 and ( ) x 7.
2.
Simplify:
Unit 3 – Part II
Period___________ Date_____________
3.
Solve the quadratic equations by factoring. a. 49𝑥 2 − 100 = 0 c.
6𝑥 2 − 11𝑥 = −5
4.
Find the vertex of the quadratic equation y
= x
2
+
4 x
-
5 . b. 𝑥
2
+ 2𝑥 − 80 = 0 d. 6𝑥
2
− 36𝑥 = 0
For Problems 5 and 6, identify how the graph of each function will be different from the parent function 𝑓(𝑥) = 𝑥 2 .
Then, answer the following questions: a.
What is the vertex? b.
What is the axis of symmetry? c.
What is the y-intercept? d.
Graph the function. e.
What are the zeros (solutions)? f.
What is the domain? g.
What is the range?
5.
𝑓(𝑥) = −(𝑥 + 2) 2 − 3 6. 𝑓(𝑥) = 2𝑥 2 + 2
Unit 3 Problems:
6. Find two consecutive positive integers such that the square of the first decreased by 17 equals 4 times the second.
7.
The sum of the squares of two consecutive integers is 85. Find the integers .
8.
If the length of one side of a square is tripled and the length of an adjacent side is increased by 10, the resulting rectangle has an area that is 6 times the area of the original square. Find the length of a side of the original square.

Algebra II Practice Test Quadratic Functions Unit 3 – Part II
9.
If the measure of one side of a square is increased by 2 centimeters and the measure of the adjacent side is decreased by 2 centimeters, the area of the resulting rectangle is 32 square centimeters. Find the measure of one side of the square.
10.
For the scenario below, use the model h
 
16 t
2  v t
0
 h
0
, where h = height (in feet), h
0
= initial height (in feet), v
0
= initial velocity (in feet per second), and t = time (in seconds).
A cheerleading squad performs a stunt called a “basket toss” where a team member is thrown into the air and is caught moments later. During one performance, a cheerleader is thrown upward, leaving her teammates’ hands 6 feet above the ground with an initial vertical velocity of 15 feet per second.
When the girl falls back, the team catches her at a height of 5 feet. How long was the cheerleader in the air?
11.
Find the inverse of the function ( ) ( x 1)
2 
5 and verify they are inverses by composition.
12.
Find the inverse of each function. Graph and label the function and its inverse. State the domain and range (in interval notation) of each function and its inverse. Determine whether the inverse is a function. a. ( )
  x

4

2 b. f x

2 x
2

3, x

0
Inverse:
Domain of function_________________
Range of function__________________
Domain of inverse_________________
Range of inverse___________________
Is inverse a function?_______
13.
Solve the quadratic inequalities.
a. 9 x
2 
16

0
Inverse:
Domain of function_____________________
Range of function_______________________
Domain of inverse______________________
Range of inverse________________________
Is inverse a function?_______ b. x
2 -
3 x
³
10

14.
Algebra II Practice Test Quadratic Functions Unit 3 – Part II
Graph the piecewise function and answer the following questions. Write domain and range in interval notation.





3, x
2
2 x 1, 2 x

2, x x

1
2
1
D f evaluate:
R f

_____________

_____________ f f
f


CALCULATOR SECTION
1.
Old Faithful in Yellowstone Park is probably the world’s most famous geyser. Old Faithful sends a stream of boiling water
into the air. During the eruption, the height h (in feet) of the water t seconds after being forced out of the ground could be
modeled by h
 
16 t 2 
150 t . a.
How long does it take the water to reach its maximum height? b. What is the maximum height of the boiling water? c. How long does it take the boiling water to reach the ground?
2.
A punter kicked a 41-yard punt. The path of the football can be modeled by y
 
0.035
x
2 
1.4
x

1 , where x is the
distance (in yards) the football is kicked and y is the height (in yards) the football is kicked. Find the maximum height of
the football. (2 pts)