Posted by **Laurie** on Tuesday, July 7, 2009 at 5:28pm.

Consider the quadratic function

f(x) = – x^2 + 10x – 26. Determine whether there is a maximum or

minimum value and find that value.

- Algebra -
**Marth**, Tuesday, July 7, 2009 at 5:34pm
This is algebra?

If you have not learned differentiation, perhaps your teacher wants you to use a calculator to find the extrema. (If you have, disregard this paragraph).

Take the derivative of f(x):

f'(x)= -2x + 10

Set f'(x) = 0

-2x + 10 = 0

10 = 2x

x = 5

Now use a sign line to find whether x=5 is a minimum or maximum.

f'(0) = +

f'(10) = -

x=5 is a maximum because f'(x) changes signs from + to -

- Algebra -
**Reiny**, Tuesday, July 7, 2009 at 5:42pm
complete the square,

f(x) = – x^2 + 10x – 26

= - [x^2 - 10x + 25 - 25] - 26

= -(x-5)^2 + 25 - 26

= -(x-5)^2 - 1

so the vertex is (5,-1) and since the parabola opens downwards, it will be a maximum point and the maximum value of the function is -1

- Algebra -
**Laurie**, Tuesday, July 7, 2009 at 5:46pm
I do not think these answers are right. I get somethin else and 5 is not an option. Here are the choices

A. Minimum is 25

B. Minimum is -51

C. Maximum is -1

D. Maximum us -51

- Algebra -
**Marth**, Tuesday, July 7, 2009 at 5:58pm
5 is the value at which the maximum occurs. f(5) = -1, so choice C.

- Algebra -
**Laurie**, Tuesday, July 7, 2009 at 5:59pm
I was thinking that as well! Thanks!

- Algebra -
**Reiny**, Tuesday, July 7, 2009 at 6:20pm
that is exactly the answer I gave you, read my last line of my reply please

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