Question

Determine the equation for the parabolas graphed below.

Answer 1

Quadratics can be written as
f(x)=a(x-h)+k
where (h,k)=coordinates of the vertex.

Here, you can read off the coordinates of the vertex and hence find h,k accordingly.
You also have the point, for example, (-5,-4) that is on the line.
This can be used to find the remaining parameter a by plugging in -5 as x and -4 as y.