Name ________________________________
Algebra 2 Exam Review Part 2 – December 2015
All correct algebraic support is required for credit. Show work on a separate piece of paper.
76. Landon was asked to solve the following system for y using substitution. His answer does not match
the teacher’s answer. In what step did Landon first make a mistake?
System of Equations:
Eq.1 : x  y  3z  8
Eq. 2 :
2 y  z  15
Eq. 3 :
3 x  2 z  7
Steps
Step 1
Procedure
Solve Eq.1 for x
Step 2
Substitute the result from step 1 into Eq.3
Step 3
Distribute the 3
Step 4
Simplify Eq. 3
Step 5
Multiply Eq. 2 by 2
Step 6
Add Step 4 and 5
Answer
Solve for y
77. What is the leading coefficient of the quadratic that
contains the points 1,4,  1,2, 3,22 ?
78. What are the vertex and the axis of symmetry of the
equation?
79. What is the vertex form of the equation?
Math
x  y  3z  8
3 y  3z  8  2z  7
3 y  9 z  24  2 z  7
 6 y  2 z  17
4 y  2 z  30
 2 y  47
y  23.5
84. Write the domain and range of the functions as an
inequality, as an interval, as set notation and on a
number line. f x   2 x 2  12 x  9
g x   3x 2  12 x  17
85. Which of the following quadratic functions have the
same vertex? f x   3x 2  12 x  1
g  x    x  2   11
hx   
k  x    x  2   13
w x   2 x  2   5
2
80. Suppose a parabola has vertex (–7, 6) and also
passes through the point (–6, 8). Write the equation
of the parabola in vertex form.
2
1
x  22  11
2
2
86. Do the graphs of y  2 x  4   3 and
2
81. Suppose a parabola has an axis of symmetry at
, a maximum height of 4 and also passes
through the point (3, 0). Write the equation of the
parabola in vertex form.
82. Rewrite the equation in vertex form. Name the
vertex and y-intercept.
83. Identify the maximum or minimum value and the
domain and range of the graph of the function
.
y  2 x 2  16 x  35 have the same vertex, yintercept, range or axis of symmetry?
87. What is an equation of a parabola with the given
vertex and focus? vertex:
; focus:
88. What is the equation, in standard form, of a
parabola that contains the following points?
(–2, 20), (0, 4), (4, 20)
89. Graph the function. How is
a
translation of
?
96. Which way do the following quadratics open when
90. Below is a table of values for a quadratic function,
h(x). Which way does the parabola open? What is
the constant term of the equation? What are the
factors of the quadratic equation? What is the
vertex of the equation?
x
h(x)
0
-5
2
3
graphed? f ( x)   x 2  2
h( x ) 
1
x  22
8
g ( y) 
1
 y  22  1
4
k ( y )   y  8   3
2
97. Which of the following quadratics has a directrix at
y  5 and an axis of symmetry at x  3 ?
6
-5
I
91. A diver jumped off of a platform and dove into the
pool. The table below shows the relationship
between the elapsed time and the height of the
diver above the pool.
Height of the diver
above the pool
(feet)
0.25
26
0.5
25
0.75
22
1
17
1.25
10
If the height of the diver is a quadratic function of time,
write an equation to represents the data in the table.
Time after the diver
jumped (seconds)
92. Below is a tabular representation of a quadratic
II
x   y  5  3
1
x  32
20
y
III
2
y
1
x  32  8
12
98. Find the solutions of the equation.
99. What is the number of real solutions?
100.
What is the number of real solutions?
101. Simplify the number using the imaginary
unit i.
102. Simplify the expression.
103. Simplify the expression.
104. Simplify the expression.
105. Simplify the expression.
106. Find the solutions of the equation.
function, f x  . Which way does the parabola
open? What is the constant term of the equation?
What are the factors of the quadratic equation?
What is the vertex of the equation? What is f 7 ?
What is the constant term? Give three ordered pairs
on the graph that are not given in the table.
x
f(x)
-3
39
-1
-1
0
-12
1
-17
2
-16
4
4
x
y
5
23
93. What are the focus and directrix of the parabola
with equation
107. Solve the inequality
108. Solve the inequality
109. Solve the inequality
the table.
?
3.5
4.5
–53.5
95. Which way does the quadratic in the table open?
x
-2
-1
-2
-5
-10
y
0
2
4
6
8
1
5
2
0
3
–3
4
–4
5
–3
6
0
7
12
110. Explain how you can use the table to help
solve the inequality
. Then solve.
94. What is the equation, in standard form, of a
parabola that models the values in the table?
x
–2
0
4
f(x)
0
12
using
x
y
111.
–3
12
–2
0
–1
–6
0
–6
1
0
2
12
Which expression is equivalent to
 5  3i    3i   2  i  ?
112. What is the real part of the simplified
expression, 2  4i  2  3i   2  i 3 ?




113. The velocity of an object in a liquid can be
modeled by the equation v  20  t  t 2 where v
is the velocity in meters per second and t is the
time in seconds. For what time interval will the
velocity be less than 14 meters per second?
114. Thomas solved a quadratic inequality by
graphing. His solution is below. What inequality
did Thomas solve?
119.
Graph the square root function. Give the domain
and range using inequalities.
120.
Graph the square root function. Identify the xand y-intercepts.
121.
How does the graph of
compare to its
parent function?
122.
Graph the relation and its inverse. Use open
circles to graph the points of the inverse.
0
4
9
10
x
y
3
2
7
–1
123.
How can you find the inverse of a function
algebraically?
115. A cell phone company predicts monthly
profit using the equation
P( x )  0.6 x 2  30 x  150 where P(x) is the
monthly profit in thousands of dollars, and x is
the amount spent on advertising in thousands
of dollars. What amount could the company
spend on advertising and still have a profit
greater than or equal to 500,000?
116. What is the vertex form of the equation?
y = x2 – 6x + 19
117. A diver jumped off of a platform and dove
into the pool. The table below shows the
relationship between the elapsed time and the
height of the diver above the pool. If the height
of the diver is a quadratic function of time,
write an equation to represent the data in the
table?
Time after the
Height of the diver
diver jumped
above the pool
(seconds)
(feet)
0.25
16.5
0.5
16
1
9
1.25
2.5
118.
Describe the domain of the function
.
Use properties of square roots to explain the domain.
124.
What is the inverse of the given relation ?
125.
Find the equation, domain, and range of the
inverse for the function
. Then graph
the inverse.
126.
Are
with domain
and
inverse functions? Explain.
127.
What is the solution of the equation?
128.
What is the solution of the equation?
129.
What is the solution of the equation?
130.
For the following question find the solution of the
equation? Eliminate any extraneous solutions.
2 x  8  x
?
131.
For
and range?
what is the domain
1
 x  5  1 to the graph of the function g  x  shown below.
3
Which of these attributes are the same for f  x  and g  x  ?
132.
133.
Compare the function f  x  
I.
domain
II.
range
III.
x-intercept
Vangie solved the following equation for x. In which step did Vangie first make a mistake?
Equation
Step 1
Step
Step
Step
Step
Step
2
3
4
5
6
Step 7

2x  8  1  x  5
 
2
2x  8  1  x  5
2x  8  1  x  5
2x  9  x  5
x9 5
x  4
Check:
2 4  8  1 
 8  8 1  1
0 1  1


2
 4  5