SOLUTION: how do you complete the square to put in the form f(x)= a(x-h)^2 +k f(x)=-x^2+4x-5

Question 750980: how do you complete the square to put in the form f(x)= a(x-h)^2 +k
f(x)=-x^2+4x-5
Answer by josgarithmetic(39623) (Show Source): You can put this solution on YOUR website!
You would add a term and subtract the same term, allowing you to convert part of the expression into a factorable square trinomial. Your given function would be handled this way:

, factor a -1

See the non-square part which is , which can be factored into . This is like a representation of a rectangle of x by (x-4) area. You could imagine cutting the longer length to leave a square area, cut the extra piece in half and put one of them along the other neighboring side of the square piece. A drawing would be better, as would be found in a few intermediate algebra books. Anyway, you will notice a missing square corner. THAT represents the term to both add and subtract symbolically.
Continuing....
You want . This is that missing square term.

=
=
=, square completed.

The standard form for your function is

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