Linear And Quadratic Functions Worksheet With Answers Page 5
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Answer Key
4.1 #29. (d)
4.1 #37c. (b)
4.3 A. (b)
4.3 #42 (c)
4.3 B. (d)
4.3 C. (a)
4.3 D. (b)
4.3 #55. (c)
4.3 #61. (c)
4.3 #62. (b)
4.3 #81. (b)
4.3 E. (d)
Solutions
4.3 A. If f (x) is a quadratic function whose graph has the vertex (h, k), which one is the
correct form of the function?
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Solution: (b)
f (x) = a(x
+ k
h)
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4.3 B. Find the vertex of the quadratic function f (x) = 2x
4x + 9.
Solution: (d)
The text gives this formula: the x-coordinate of the vertex of the graph
2
b
of f (x) = ax
+ bx + c is x =
. In this example, a = 2 and b =
4, so the vertex occurs
2a
4
at x =
= 1. Then f (1) = 2
4 + 9 = 7 gives the y-coordinate.
2·2
If you forget the formula, you can always complete the square:
2
2
2
2
f (x) = 2x
4x + 9 = 2(x
2x) + 9 = 2(x
2x + 1) + 9
2 = 2(x
1)
+ 7
so h = 1 and k = 7 and the vertex is (1, 7).
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4.3 C. Find the axis of symmetry of the graph of f (x) = 4x
8x + 3.
Solution: (a)
The axis of symmetry passes through the vertex, which has x-coordinate
8
= 1. The axis of symmetry is the line x = 1.
2·4
Again, if you forget the formula, complete the square:
2
2
2
2
f (x) = 4x
8x + 3 = 4(x
2x) + 3 = 4(x
2x + 1) + 3
4 = 4(x
1)
1
This shows that the vertex is at (1, 1).
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4.3 D. Let f (x) = 4x
8x + 3. Find the x and y-intercepts, if any.
Solution: (b)
Since f (0) = 3, the y-intercept is (0, 3).
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To find the x-intercept, solve 4x
8x + 3 = 0. This can be factored as 4x
8x + 3 =
3
1
(2x
1)(2x
3), so 2x
1 = 0 or 2x
3 = 0, giving the x-intercepts (
, 0) and (
, 0).
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