A parabola with vertex at $(1, −2)$ passing through $(0, 0)$ and $(2, 0)$

Question

I know how to find a parabola passing through $(0, 0)$ and $ (2, 0)$:

$y=x(x-2)$

I also know how to find a parabola with vertex at $(1, −2)$: $(x-1)^2-2$

But I don't know how to find a parabola with both vertex at $(1, −2)$ passing through $(0, 0)$ and $(2, 0)$?

Answer 1

A parabola passing through $\left(0,0\right)$ and $\left(2,0\right)$ has also the form $y=ax(x-2)$, then you can put in $\left(-2,1\right)$ to find $a$.

Also, you can take the form $y=c(x-1)^2-2$ and plug in $\left(0,0\right)$