MAT-121: COLLEGE ALGEBRA
Written Assignment 4
2.5 points each
SECTION 5.1
Algebraic
For the following exercise, rewrite the quadratic function in standard form and give the vertex.
1.
y
=
4
x
2
+
5
x
−
7
h
=
−
5
2
(
4
)
h
=
−
5
8
k
=
4
(
−
5
8
)
2
+
5
(
−
5
8
)
−
7
k
=
4
(
25
64
)
+
5
(
−
5
8
)
−
7
k
=
25
16
−
25
8
−
7
k
=
25
16
−
50
16
−
112
16
k
=
−
137
16
Vertex:
(
−
5
8
,
−
137
16
For the following exercise, determine whether there is a minimum or maximum value to the quadratic
function. Find the value and the axis of symmetry.
2.
y
=
1
3
x
2
−
4
x
+
9
h
=
4
2
3
h
=
6
Minimum is -3 which occurs at 6.
k
=
1
3
(
6
)
2
−
4
(
6
)
+
9
k
=
12
−
24
+
9
k
=−
3
Axis of symmetry: x = 6
)
Copyright © 2019 by Thomas Edison State University. All rights reserved.

For the following exercise, rewrite the quadratic function in standard form and give the vertex. Determine
whether there is a minimum or maximum value to the quadratic function. Find the value and the axis of
symmetry. Determine the domain and range of the quadratic function.

For the following exercise, use the vertex (h, k) and a point on the graph (x, y) to find the general form of
the equation of the quadratic function.

5.
An athletic stadium holds 105,000 fans. With a ticket price of $22, the average attendance has
been 32,000. When the price dropped to $16, the average attendance rose to 50,000. Assuming
that attendance is linearly related to ticket price, what ticket price would maximize revenue?
Round ticket price to the nearest ten cents.

Copyright © 2019 by Thomas Edison State University. All rights reserved.

h
=
−
98000
2
(−
3000
)
h
=
$
16.33
Copyright © 2019 by Thomas Edison State University. All rights reserved.

SECTION 5.2
Algebraic
For the following exercise, identify the function as a power function, a polynomial function, or neither.
6.
f
(
x
)=
4
(
x
3
)
3
Power function
For the following exercise, find the degree and leading coefficient for the given function if it is a
polynomial. If it is not a polynomial, then state so.
7.
f
(
x
)=
(
2
x
2
−
5
)
2
+
(
x
−
3
)
2
+
5
f
(
x
)
=
(
2
x
2
−
5
) (
2
x
2
−
5
)
+
(
x
−
3
) (
x
−
3
)
+
5
f
(
x
)
=
4
x
4
−
19
x
2
−
6
x
+
39
Leading coefficient & leading degree are both 4.
For the following exercise, find the intercepts of the functions.
8.
g
(
x
)=
(
3
x
2
−
10
x
−
8
)
(
x
+
3
)
g
(
0
)
=
(
3
(
0
)
2
−
10
(
0
)
−
8
)
(
0
+
3
)
g
(
0
)
=−
24
y
−
intercept is
(
0
,
−
24
)
0
=
(
3
x
2
−
10
x
−
8
)
(
x
+
3
)
0
=
(
x
−
4
) (
3
x
+
2
) (
x
+
3
)
0
=
x
−
4
x
−
intercepts are
(
4,0
)
x
=
4
0
=
3
x
+
2
x
=
−
2
3
0
=
x
+
3
x
=−
3
(
−
2
3
,
0
)
,
∧
(
−
3,0
)
Technology
For the following exercise, graph the polynomial function using a calculator or a graphing utility. Based on
the graph, determine the intercepts and the end behavior.
9.
f
(
x
)=
x
6
−
36
x
−
intercepts
:
(
−
1.81,0
) (
1.81,0
)
y
−
intercept
:
(
0
,
−
36
)
x→
−
∞, f
(
x
)
→∞
¿
x→∞ ,f
(
x
)
→∞
Copyright © 2019 by Thomas Edison State University. All rights reserved.

Real-World Applications