Question

The vertex if the parabola below is at the point (3,-3) and the point (0,-2) is on the parabola . Write the equation of the parabola.

Answer 1

If we know the vertex, then, that means:
\[
y=a(x-x_0)^2+y_0\implies\\
y=a(x-3)^2-3
\]And, we plug in values to find \(a\):
\[
\begin{align}
-2&=a(0-3)^2-3\implies\\
-2&=9a-3\implies\\
1&=9a\implies\\
a&=\frac{1}{9}
\end{align}
\]Therefore, our formula is:
\[
y=\frac{1}{9}(x-3)^2-3
\]

Answer 2

Thank you <3