Question

How to find the equation of a Parabola with vertex (0,-9) and passing through (6,-8)?

Answer 1

`y = x^2/36 -9`

Explanation:

The general vertex form for a parabola is
`color(white)("XXXX")` `y = m(x-a)^2+b`
`color(white)("XXXX")` `color(white)("XXXX")`where the vertex is at `(a,b)`

Given that the vertex of the desired parabola is at `(0,-9)`
this becomes:
`color(white)("XXXX")` `y = m(x-0)^2-9`

and since `(x,y) = (6,-8)` is a solution point on this parabola:
`color(white)("XXXX")` `-8 = m(6-0)^2-9`

`color(white)("XXXX")` `1 = 36m`

`color(white)("XXXX")` `m = 1/36`

Therefore
`color(white)("XXXX")` `y = 1/36(x-0)^2-9`
or
`color(white)("XXXX")` `y = x^2/36 -9`