Thread: Proving functions

Hey all, I just have a homework problem example that I can't even begin.

it says:

Prove {-x^2+6x-8 x is in Reals} = (- ∞, 1]


I'm not even sure what to do, even looking in my notes and online didn't really help me, thought I'd give this place a try, thanks guys!

Originally Posted by teacast

Hey all, I just have a homework problem example that I can't even begin.

it says:

Prove {-x^2+6x-8 x is in Reals} = (- ∞, 1]


I'm not even sure what to do, even looking in my notes and online didn't really help me, thought I'd give this place a try, thanks guys!

You are asked to find the range of the function:



The graph of the function is a parabola opening down, thus the vertex V(3, 1) is the maximum point and all values of y are equal or smaller than 1. Therefore

Oh okay, just one question... why did you add a -1 to ? Just a way to say adding 8 so you could make it factorable?

Thanks for the help!

Originally Posted by teacast

Oh okay, just one question... why did you add a -1 to ? Just a way to say adding 8 so you could make it factorable?

Thanks for the help!

He didn't' add -1 to anything. Her wrote the 8 as 9- 1 (which he can do because 8= 9- 1 so that he would have a perfect square,

What he did is called "completing the square".

ohhh okay okay, that's sort of what I meant, thanks for the clarification!