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HACTEHA [7]
2 years ago
6

A. Rewrite the function y = x2 – 14x + 58 in vertex form by completing the square. Show your work. B. Rewrite the function y = –

x2 – 6x – 20 in vertex form by completing the square. Show your work. C. Does the function y = x2 – 14x + 58 have a maximum or a minimum, and what is it? How about the function y = –x2 – 6x – 20? Explain your answers.

Mathematics
1 answer:
marysya [2.9K]2 years ago
8 0

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.

___

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

__

B. y = -x² -6x -20

y = -(x² +6x) -20

y = -(x² +6x +9) -20 -(-9)

y = -(x +3)² -11

__

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.

___

D. The function of part B has a maximum at the vertex (-3, -11). -11 is the maximum value.

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klio [65]

Answer:

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Step-by-step explanation:

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The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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Step-by-step explanation:

5 0
2 years ago
Your instructor has 50 questions on a quiz and the are 2 points a peice. The maxium score is 100. and you miss 11 of these quest
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Answer:

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Step-by-step explanation:

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6 0
3 years ago
Read 2 more answers
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