Math Help - increasing decreasing

1. increasing decreasing

Find the intervals on which y = (x +4)^2 - 7 is increasing or decreasing

I have never had a problem like this i don't know what to do please help
thank you!

2. where did the 9 come from?

3. Originally Posted by aikenfan
Find the intervals on which y = (x +4)^2 - 7 is increasing or decreasing

I have never had a problem like this i don't know what to do please help
thank you!
Originally Posted by aikenfan
where did the 9 come from?
$y = (x + 4)^2 - 7 = (x^2 + 8x + 16) - 7 = x^2 + 8x + 9$

-Dan

4. Originally Posted by aikenfan
Find the intervals on which y = (x +4)^2 - 7 is increasing or decreasing

I have never had a problem like this i don't know what to do please help
thank you!
Actually there's a quicker way. A (vertical) parabola has the form:
$y = a(x - h)^2 + k$
where the vertex is at (h, k) and it opens upward if a > 0 and opens downward if a < 0.

So the vertex of $y = (x + 4)^2 - 7$ is at (-4, -7) and a = 1. Thus it opens upward. So it must be decreasing on $( - \infty, -4)$ and increasing on $(-4, \infty)$.

-Dan