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Annette [7]
3 years ago
13

How do I Rewrite the function by completing the square x^2+8x-29

Mathematics
1 answer:
Flura [38]3 years ago
5 0

Answer:

  (x +4)^2 -45

Step-by-step explanation:

The square of a binomial has the form ...

  (x +a)^2 = x^2 +2ax +a^2

That is, the constant term (a^2) is the square of half the coefficient of the linear term: (2a/2)^2 = a^2.

To "complete the square", you add 0 in the form of the desired constant added to its opposite. Here, we want the constant for the square to be (8/2)^2 = 16. So, we can add 0 = 16 -16 to the expression:

  x^2 +8x +16 -29 -16

  (x^2 +8x +16) -45 . . . . group the terms that make the square

  (x +4)^2 -45 . . . . rewritten after completing the square

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5 0
3 years ago
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Semenov [28]

Answer:

<em>The difference quotient of f is 8. </em><em>Option C</em>

Explanation:

<u>Difference Quotient</u>

Given a function f(x), the difference quotient is defined as

\displaystyle d=\frac{f(h+h)-f(x)}{h},\ h\neq 0

The function provided in the question is

f(x)=8x+1

Find f(x+h) by substituting x by x+h:

f(x+h)=8(x+h)+1

f(x+h)=8x+8h+1

Now compute:

\displaystyle d=\frac{8x+8h+1-(8x+1)}{h}

Operating:

\displaystyle d=\frac{8x+8h+1-8x-1}{h}

Simplifying:

\displaystyle d=\frac{8h}{h}

d=8

A.  Incorrect.

This choice is different from the answer.

B. Incorrect.

This choice is different from the answer.

C. Is correct

The difference quotient is 8 as explained above.

D. Incorrect.

This choice is different from the answer.

4 0
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