Mathematics Algebra II Unit 05: Quadratic Functions, Equations, and Inequalities
2013­2014
This document is the property of the TCMPC and as such may not be replicated or changed without permission.
1 Find the discriminant and determine the
nature of the roots:
3 Simplify:
4x2 = 8x ­13
(Assume denominator is not equal to zero.)
A
B
A 0; one real
B
144; two real rational
C
3120; two real irrational
C
D
D ­144; two imaginary
2 The path of a toy rocket launched from an
observation tower is modeled by the
4 Solve for x:
equation h(t) = ­16t 2 + 48t + 64 where t
is time in seconds, and h is height in feet.
In how many seconds will the toy rocket
first reach 90 feet?
F
G
H
J
Page 2
GO ON
This document is the property of the TCMPC and as such may not be replicated or changed without permission.
5 Describe the root(s) of the quadratic
8 Solve 0= 7x2 ­ 253x ­ 1700 to the nearest
equation graphed below:
hundredth.
9 Find the discriminant and describe the
roots of 6x2 ­ 10x + 1 = 0.
A two real rational roots
B
two real irrational roots
C
two imaginary roots
D one real root
10
6 The function y = ­64(x ­ 3)2 + 400, models
Marcos is building a rectangular pen for
animals, using the side of a barn as one
a store's profits in dollars on a certain food
side. He has 200 feet of fencing to use
item where x is the price of the item. What
for the other 3 sides. What is the
should the store charge for the item to
maximum area that he can enclose?
maximize the profit? What is the maximum
possible profit that can be earned
according, to the model?
11
How does the graph of y = ­4x2 compare
to the graph of y = x2?
7 Greg is looking at the graph of a parabola.
Its vertex is (2, ­144), it intersects the x­
axis at ­4 and 8, and it intersects the y­
axis at ­128. What are the roots of the
equation he has graphed?
A 2 and ­144
B
­4, 8, and ­128
C
­4 and 8
D 4 and ­8
Page 3
GO ON
This document is the property of the TCMPC and as such may not be replicated or changed without permission.
12
Write a quadratic function in the form
y = x2 + bx + c whose graph opens
upward and has roots of 13
.
When asked to solve the inequality
x2 ≥ 8x ­ 16 , Kevin thought about its
graph and responded that x could be any
real number. Was he correct? Why or why
not?
14
Find the vertex for the function:
y = x2 + 4x ­ 7
15
F
(4,1)
G
(­4,­1)
H
(­2,­3)
J
(­2,­11)
Use the table of values for the quadratic
function below to determine between
which two x values f(x) will have a zero.
x
2
5
8
11
14
f(x) ­2
­5
10
43
94
A between 11 and 14
B
between 8 and 11
C
between 5 and 8
D between ­2 and 5
Page 4
STOP
This document is the property of the TCMPC and as such may not be replicated or changed without permission.
Test Key
Mathematics Algebra II Unit 05: Quadratic Functions, Equations, and Inequalities 2013-2014
##
Item #
Correct Answer
Primary
SE
Secondary
SE
Obj/Cat
1
MA200076RX
D
A2.8(B) [S]
None
STAAR: Algebra II
3
2
MA21085380D
approximately 0.7 seconds
A2.6(A) [R]
None
STAAR: Algebra II
3
3
MA200168RX
C
A2.2(A) [S]
None
STAAR: Algebra II
2
4
MA200185RX
G
A2.2(B) [S]
None
STAAR: Algebra II
2
5
MA200189RX
C
A2.2(B) [S]
None
STAAR: Algebra II
2
6
MA21085385D
The store should charge $3; the maximum profit would be
$400.
A2.6(A) [R]
None
STAAR: Algebra II
3
7
MA200104RX
C
A2.8(C) [S]
None
STAAR: Algebra II
3
8
MA21085395D
-5.79 and 41.93
A2.8(D) [R]
None
STAAR: Algebra II
3
9
MA21085393D
76; two real irrational roots
A2.8(B) [S]
None
STAAR: Algebra II
3
10
MA21085391D
5000 square feet
A2.8(A) [R]
None
STAAR: Algebra II
3
11
MA21085389D
A2.7(B) [S]
None
STAAR: Algebra II
4
12
MA200256RX
A2.6(C) [S]
None
STAAR: Algebra II
3
A2.6(A) [R]
None
STAAR: Algebra II
3
It is narrower and opens downward or reflected across
x - axis and stretched by a factor of 4.
y = x2 - 10x + 22
Yes, he was correct. x2 ≥ 8x - 16 is equivalent to
13
MA200244RX
14
MA21085387D
J
A2.7(A) [R]
None
STAAR: Algebra II
4
15
MA200079RX
C
A2.6(B) [R]
None
STAAR: Algebra II
3
x2 - 8x + 16 ≥ 0. The domain of the graph will be all real
numbers.
This document is the property of the TCMPC and as such may not be replicated or changed without permission.