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School
Liberty University *
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Course
ALGEBRA
Subject
Mathematics
Date
Feb 20, 2024
Type
Pages
27
Uploaded by keelydrewry
An Olympic pole vaulter's height can be modeled by the equation
f
(
x
) = −16
x
2
+ 32
x
, where
x
is the time in
seconds after the vaulter leaves the ground. Find the vaulter's maximum height and the time it takes the
vaulter to reach this height. Then find how long the vaulter is in the air.
At 1 second, the vaulter has reached a maximum height of 48 feet. The vaulter is in the air for 2 seconds.
At 2 seconds, the vaulter has reached a maximum height of 16 feet. The vaulter is in the air for 4
seconds.
At 2 seconds, the vaulter has reached a maximum height of 32 feet. The vaulter is in the air for 4
seconds.
At 1 second, the vaulter has reached a maximum height of 16 feet. The vaulter is in the air for 2
seconds.
f
(
x
) = −16
x
2
+ 32
x
Step 1
Find the axis of symmetry.
The axis of symmetry is
x = 1
.
Step 2
Find the vertex.
y
= −16(
1
)
2
+ 32(
1
)
y
= −16 + 32
y
= 16
The vertex is
(1, 16)
.
The vaulter's maximum height is 16 ft and it takes 1 s to reach this height.
The vaulter takes the same time to fall back to the ground. Therefore the vaulter is
in the air for 2 s.
12
/ 12
Question 2 : 11 pts
Graph
y
= −3
x
2
− 3
x
+ 1.
Graph
y
= −3
x
2
− 3
x
+ 1.
y
= −3
x
2
− 3
x
+ 1
Step 1
Find the axis of symmetry.
The axis of symmetry is
x = −1/2
.
Step 2
Find the vertex.
y
= −3(
−1/2
)
2
− 3(
−1/2
) + 1
y
= −3/4 + 6/4 + 4/4
y
= 7/4
The vertex is
(−1/2, 7/4)
.
Step 3
Find the
y
-intercept.
y
= −3(0)
2
− 3(0) + 1
y
= 1
The
y
-intercept is
1
; the graph passes through (0,
1
).
Step 4
Find two more points on the same side of the axis of symmetry as the point
containing the
y
-intercept.
y
= −3(0
.
5)
2
− 3(0
.
5) + 1 = −1
.
25
y
= −3(1)
2
− 3(1) + 1 = −5
Two other points are (
0
.
5, −1
.
25
) and (
1, −5
).
Step 5
Graph the
axis of symmetry
, the
vertex
, the point containing the
y
-intercept
, and
two other points
.
Step 6
Reflect the points across the axis of symmetry. Connect the points with a
smooth curve.
11
/ 11
Question 3 : 11 pts
Identify the graph of the quadratic function
y
=
x
2
+ 6
x
+ 7.
Identify the graph of the quadratic function
y
=
x
2
+ 6
x
+ 7.
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