College Algebra 9th txtbk

SECTION 3–4 Quadratic Functions 219
In Problems 61–68, find the standard form of the equation for the
quadratic function whose graph is shown.
61.
y
66.
9
y
(1, 4)
5
(3, 4)
(0, 5)
5
5
x
(1, 0)
5
1
(5, 0)
x
5
62.
5
y
(1, 4)
67.
y
5
(0, 2.5)
5
(1, 0) (5, 0)
3
7
x
5
(3, 1)
(1, 1)
5
x
5
63.
(2, 4)
5
y
68.
y
5
(0, 2.5)
5
(1, 4)
(3, 2) (1, 2)
(5, 0)
8
(1, 0)
2
x
5
5
x
5
64.
65.
5
y
5
(3, 3)
(0, 0) (6, 0)
2
8
5
y
5
(1, 0) (3, 0)
5
5
(0, 3)
5
x
x
In Problems 69–74, find the equation of a quadratic function
whose graph satisfies the given conditions.
69. Vertex: (4, 8); x intercept: 6
70. Vertex: (2, 12); x intercept: 4
71. Vertex: (4, 12); y intercept: 4
72. Vertex: (5, 8); y intercept: 2
73. Vertex: (5, 25); additional point on graph: (2, 20)
74. Vertex: (6, 40); additional point on graph: (3, 50)
75. For f(x) a(x h) 2 k, expand the parentheses and simplify
to write in the form f(x) ax 2 bx c. This proves
that any function in vertex form is a quadratic function as defined
in Definition 1.
76. Find a general formula for the constant term c when expanding
f(x) a(x h) 2 k into the form f(x) ax 2 bx c.
77. Let g(x) x 2 kx 1. Graph g for several different values
of k and discuss the relationship between these graphs.
78. Confirm your conclusions in Problem 77 by finding the vertex
form for g.