Finding The Maximum Using The Vertex Worksheet With Answer Key Page 3
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1
2
3
4
52
R = 800 – 40x + 200x – 10x
2
R = -10x
+ 160x + 800
b
Use the formula
=
−
to help find the vertex.
p
2a
2
R = -10x
+ 160x + 800
a = -10, b = 160
b
160
=
−
=
−
=
So the vertex is (8, ???)
p
8
−
2a
( 2
10
)
2
Substitute 8 in for x in the equation R = -10x
+ 160x + 800 to find the other part of the vertex.
2
R = -10(8)
+ 160(8) + 800
R = -640 + 1280 +800
R = 1440
So the vertex is (8, 1440)
This means there are 8 increases of $2 with a maximum revenue of $1440.
The new price will be 8 + 2x = 8 + 2(8) = $24
The number of shorts sold will be 100 – 5x = 100 – 5(8) = 60 shorts
Graph:
R
1600
1400
1200
1000
800
600
400
200
0
-8
-4
-24 -20 -16 -12
0
4
8
12
16
20
24
x
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