Answer:
A. y = (x -7)² +9
B. y = -(x +3)² -11
C. minimum, (7, 9)
D. maximum, (-3, -11)
Step-by-step explanation:
The general steps to rewriting the function in vertex form are ...
1. factor out the leading coefficient (if not 1) from the first two terms
2. add inside parentheses the square of half the x coefficient; subtract the same amount outside parentheses. The factor in front of the parentheses must be taken into account when adding the same amount outside.
3. rewrite the content of parentheses as a square, collect terms outside parentheses.
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A. y = x² -14x +58
y = (x² -14x) +58 . . . . . . . . . . step 1
y = (x² -14x +49) +58 -49 . . . step 2
y = (x -7)² +9 . . . . . . . . . . . . . step 3
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B. y = -x² -6x -20
y = -(x² +6x) -20
y = -(x² +6x +9) -20 -(-9)
y = -(x +3)² -11
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C. In vertex form, the function for vertical scale factor "a" and vertex (h, k) looks like ...
y = a(x -h)² +k
When a < 0, the vertex is a maximum (the graph opens downward); when a > 0, the vertex is a minimum (the graph opens upward).
The function of part A has a minimum at the vertex (7, 9). 9 is the minimum value.
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D. The function of part B has a maximum at the vertex (-3, -11). -11 is the maximum value.
