Linear And Quadratic Functions Worksheet Page 7
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1
2
3
4
5
6
7
8
9214
Linear and Quadratic Functions
y
2
2
5
73
8. f (x) =
3x
+ 5x + 4 =
3 x
+
6
12
6
5
73
5+ 73
x-intercepts
, 0 and
, 0
6
6
5
y-intercept (0, 4)
4
Domain: (
,
)
3
73
Range:
,
12
5
2
Increasing on
,
6
5
Decreasing on
,
1
6
5
73
Vertex
,
is a maximum
6
12
1
1
2
3
x
5
Axis of symmetry x =
1
6
2
3
2
1
1
40001
2
9. f (x) = x
x
1 = x
100
200
40000
y
1+ 40001
1
40001
x-intercepts
and
8
200
200
y-intercept (0, 1)
7
6
Domain: (
,
)
5
40001
Range:
,
4
40000
1
3
Decreasing on
,
200
2
1
Increasing on
,
1
200
1
40001
12
Vertex
,
is a minimum
x
200
40000
2
1
1
2
1
Axis of symmetry x =
200
• P (x) =
2
10.
2x
+ 28x
26, for 0
x
15.
• 7 T-shirts should be made and sold to maximize profit.
• The maximum profit is $72.
• The price per T-shirt should be set at $16 to maximize profit.
• The break even points are x = 1 and x = 13, so to make a profit, between 1 and 13
T-shirts need to be made and sold.
• P (x) =
2
11.
x
+ 25x
100, for 0
x
35
• Since the vertex occurs at x = 12.5, and it is impossible to make or sell 12.5 bottles of
tonic, maximum profit occurs when either 12 or 13 bottles of tonic are made and sold.
• The maximum profit is $56.
• The price per bottle can be either $23 (to sell 12 bottles) or $22 (to sell 13 bottles.)
Both will result in the maximum profit.
• The break even points are x = 5 and x = 20, so to make a profit, between 5 and 20
bottles of tonic need to be made and sold.
12
You’ll need to use your calculator to zoom in far enough to see that the vertex is not the y-intercept.
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