Question

What is the equation of the parabola that has a vertex at `(-2, -4)` and passes through point `(-3,-5)`?

Answer 1

`y=-(x+2)^2-4`

Explanation:

The general vertex form of a parabola with vertex at `(a,b)` is
`color(white)("XXX")y=m(x-a)^2+bcolor(white)("XXX")` for some constant `m`

Therefore a parabola with vertex at `(-2,-4)` is of the form:
`color(white)("XXX")y=m(x+2)^2-4color(white)("XXX")` for some constant `m`

If `(x,y)=(-3,-5)` is a point on this parabola
`color(white)("XXX")-5 = m(-3+2)^2-4`

`color(white)("XXX")-5 = m - 4`

`color(white)("XXX")m=-1`

and the equation is `y=1(x+2)^2-4`
graph{-(x+2)^2-4 [-6.57, 3.295, -7.36, -2.432]}