How do you find the vertex of y= -x^2 -3?

1 Answer
Apr 27, 2018

So we know that in the equation y=a(x-d)^2+e, the vertex is (d,e) because it's a parabola. We know that a=-1 because the the only way to get -x^2 is by doing ax^2, so ax^2=-x^2, so a = -1.

We also have that -2adx=0x because there is no x factor and the only way to get something with only one x in it is by using -2adx. If -2adx=0x, we can divide both sides by -2x to get ad=0. For this to be true, then either a or d has to be 0, but we already know that a is -1, so d=0.

Now the only way to get a number with no x in it is ad^2+e, so ad^2+e=-3. We know that a and d are -1 and 0, respectively, so we replace the variables to get e=-3. We know that the vertex is (d,e), so we replace the variables to get that the vertex is (0,-3).