How do you find the vertex of y=−x2−3?

1 Answer
Soul of Fire
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 −x2 is by doing ax2, so ax2=−x2, 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 ad2+e, so ad2+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).

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