Relating The Standard And Factored Forms Worksheet - Chapter 3.2 Page 2
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113.2
1
Connecting the standard and factored
EXAMPLE
forms of quadratic functions
Compare the two functions:
R(x) 5 (40 2 x) (10 1 x)
R(x) 5 2x
1 30x 1 400
2
and
Enrique’s Solution: Comparing and Analyzing the Graphs
Rachel’s Function
Andrew’s Function
R(x) 5 (40 2 x)(10 1 x)
R(x) 5 2x
1 30x 1 400
2
x
x
5 (40 2 0)(10 1 0)
5 20
1 30(0) 1 400
2
0
0
5 (40)(10)
5 0 1 0 1 400
5 400
5 400
4
504
4
504
8
576
8
576
12
616
12
616
16
624
16
624
20
600
20
600
24
544
24
544
Revenue from T-shirt Sales
R(x)
The tables of values are the same
600
for both functions, so the graphs
500
will be the same. I need only one
graph.
400
I used Rachel’s table of values to
300
make a graph.
200
The two functions are equivalent.
100
x
0
5
10
15 20
25
Number of $1 increases
To get the maximum revenue,
The maximum revenue is
I looked at my graph and found
about $625.
the y-coordinate of the vertex.
Since the vertex occurs at
(15, 625)
, R(15) 5 625.
133
Working with Quadratic Functions: Standard and Factored Forms
NEL
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