find the intervlas increaseing and decreasing for -x^2+8x+20?

Answer 1

I agree with first answer. Another way to see this is to take the derivative of f(x) = -x^2 +8x + 20

to get f'(x) = -2x + 8

The original function is decreasing when f'(x) < 0, that is, when
-2x + 8 < 0 or x>4.

The original function is increasing when f'(x) > 0, that is, when
-2x + 8 > 0 or x<4

Answer 2

This is a parabola that increases from - infinity to a max value and then decreases to - infinity. You know it's a max because the x^2 term is negative. The axis of symmetry is x = -b/2a = -8/-2 = 4.

So the parabola increases (-infinity,4) and decreases over
(4, + infinity)