SOLUTION: Explain why the graph of the equation g(x)=-(x+1)^2-3 would be a parabola opening downward. The parabola opens downwards since a= and this value is 0.

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Question 1165515: Explain why the graph of the equation g(x)=-(x+1)^2-3 would be a parabola opening downward.
The parabola opens downwards since a= and this value is 0.
Found 2 solutions by greenestamps, Edwin McCravy:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The general equation in vertex form is

g%28x%29+=+a%28x-h%29%5E2%2Bk

The parabola opens upward if a>0 and downward if a<0.

In this example, a=-1, which is less than 0, so the parabola opens downward.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Your error is that "a" is not 0, it's -1, because if you square the
parentheses and collect terms, you get

%22g%28x%29%22=-%28x%2B1%29%5E2-3

%22g%28x%29%22=-%28x%2B1%29%28x%2B1%29-3

%22g%28x%29%22=-%28x%5E2%2Bx%2Bx%2B1%29-3

%22g%28x%29%22=-%28x%5E2%2B2x%2B1%29-3

The - sign changes all the signs inside the parentheses:

%22g%28x%29%22=-x%5E2-2x-1-3

%22g%28x%29%22=-x%5E2-2x-4

%22g%28x%29%22=-1x%5E2-2x-4

So you see "a" is not 0, it's -1.

I multiplied it all out to show you that a =-1, not 0. But you 
can tell it is -1 without multiplying it out if you think about it.

Edwin