Question

What is the equation of the parabola that has a vertex at `(-14, 2)` and passes through point `(0,-17)`?

Answer 1

`y=-19/196(x+14)^2+2`

Explanation:

`y=a(x-h)^2+k`=> equation of parabola in vertex form where`(h, k)` is the vertex, then in this case:
`y=a(x+14)^2+2` => substitute`(x, y)=(0,-17)` to solve for `a`:
`-17=a(0+14)^2+2` => simplify:
`-19=196a`
`a=-19/196`
hence the equation is:
`y=-19/196(x+14)^2+2`