Question

what's the range of y=- x^2+3

Answer 1

It's a parabola so it's going to have a minimum of maximum somewhere.

Answer 2

Since it's \(-x^2\) the negative makes it concave down... meaning it will have a maximum somewhere. If we find the maximum to be \(a\), then we know the range is \((-\infty,a]\).

Answer 3

You can find where this maximum is by converting it into vertex form...
Fortunately, it's easy to see: \[
y = -(x-0)^2+3
\]Meaning our vertex is at \((1,3)\)... So \(a=3\)...

Answer 4

Whoops, I mean the vertex is at \((0,3)\).

Answer 5

Giving us a range of\[
(-\infty,3]
\]