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The function f is defined above. Which of the following equivalent for

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Arick
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The function f is defined above. Which of the following equivalent for [#permalink] New post   Updated on: 05 Jun 2023, 19:05
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f(x) = -x²+6x+20

The function f is defined above. Which of the following equivalent forms of f(x) displays the maximum value of f as a constant or coefficient?

(A) f(x) = (x-3)²+11

(B) f(x) = -(x-3)²+29

(C) f(x) = -(x+3)² + 11

(D) f(x) = (x+3)² +29

(E) f(x) = -(x-3)²-11

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B

Originally posted by Arick on 05 Jun 2023, 02:30.
Last edited by Arick on 05 Jun 2023, 19:05, edited 1 time in total.
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imorenor
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Re: The function f is defined above. Which of the following equivalent for [#permalink] New post   05 Jun 2023, 17:43
Why is option B the correct answer?

f(x) = (x-3)²+29
f(x) = (x²-6x+9)+29
f(x) = x²-6x+38 <>-x²+6x+20

shouldn't it be the correct answer?
f(x) = -(x-3)²+29
f(x) = -(x²-6x+9)+29
f(x) = -x²+6x-9+29
f(x) = -x²+6x+20
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The function f is defined above. Which of the following equivalent for [#permalink] New post   05 Jun 2023, 20:36
Given: f(x) = -x²+6x+20

The function f is defined above.

Asked: Which of the following equivalent forms of f(x) displays the maximum value of f as a constant or coefficient?

\(f(x) = -x²+6x+20 = - (x^2 - 6x + 9) +9 + 20 = -(x-3)^2 + 29\)

IMO B
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Re: The function f is defined above. Which of the following equivalent for [#permalink] New post   07 Jun 2023, 17:43
Arick wrote:
f(x) = -x²+6x+20

The function f is defined above. Which of the following equivalent forms of f(x) displays the maximum value of f as a constant or coefficient?

(A) f(x) = (x-3)²+11

(B) f(x) = -(x-3)²+29

(C) f(x) = -(x+3)² + 11

(D) f(x) = (x+3)² +29

(E) f(x) = -(x-3)²-11

Posted from my mobile device


I didnt quite understand the qs. Can someone pls help?
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Re: The function f is defined above. Which of the following equivalent for [#permalink] New post   08 Jun 2023, 00:47
RenB wrote:
Arick wrote:
f(x) = -x²+6x+20

The function f is defined above. Which of the following equivalent forms of f(x) displays the maximum value of f as a constant or coefficient?

(A) f(x) = (x-3)²+11

(B) f(x) = -(x-3)²+29

(C) f(x) = -(x+3)² + 11

(D) f(x) = (x+3)² +29

(E) f(x) = -(x-3)²-11

Posted from my mobile device


I didnt quite understand the qs. Can someone pls help?



The question wants us to convert the given equation in a form in which the MAX value of the function is visible .

But we don't know what is the MAX value. To find that we have to convert the existing equation in some (a+b)^2 or (a-b)^2 form as shown below:

f(x) = -x²+6x+20
f(x) = -x²+6x-9+29
f(x) = -(x²-6x+9)+29
f(x) = -(x-3)²+29 --> Now we can see this will give max value when the constant (29) is not subtracted by any number . The MAX value is 29.
We see that this equation already has the max value in it. So this is our required answer.

Correct Option - (B)
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Re: The function f is defined above. Which of the following equivalent for [#permalink]
08 Jun 2023, 00:47
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