Math 095 - Intermediate Algebra - Prairie State College

Objective 19: Graph quadratic functions. Find vertices and x- and y-intercepts of parabolas.
50. The function f is written below in two different, but equivalent, forms:
f(x) = 2(x − 2) 2 + 3 f(x) = 2x 2 − 8x + 11
Using either one of the forms for f, sketch the graph of f.
(a)
y
(b)
y
8
8
6
6
4
4
2
-8 -6 -4 -2 2 4 6 8
-2
x
2
-8 -6 -4 -2 2 4 6 8
-2
x
-4
-4
-6
-6
-8
-8
(c)
y
(d)
y
8
8
6
6
4
4
2
-8 -6 -4 -2 2 4 6 8
-2
x
2
-8 -6 -4 -2 2 4 6 8
-2
x
-4
-4
-6
-6
-8
-8
51. Which of the following is an equation for a parabola that opens up and has vertex
(−4, 5) (Each equation is written in two different, but equivalent, forms.)
(a) y = (x − 4) 2 + 5 or y = x 2 − 8x + 21
(b) y = (x + 4) 2 + 5 or y = x 2 + 8x + 21
(c) y = −(x + 4) 2 − 5 or y = −x 2 − 8x − 21
(d) y = −(x − 4) 2 − 5 or y = −x 2 + 8x − 21
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