Algebra
posted by Laurie .
Consider the quadratic function
f(x) = – x^2 + 10x – 26. Determine whether there is a maximum or
minimum value and find that value.

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  
complete the square,
f(x) = – x^2 + 10x – 26
=  [x^2  10x + 25  25]  26
= (x5)^2 + 25  26
= (x5)^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 
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 
5 is the value at which the maximum occurs. f(5) = 1, so choice C.

I was thinking that as well! Thanks!

that is exactly the answer I gave you, read my last line of my reply please