Question

What is the equation of the parabola that has a vertex at `(-8, 5)` and passes through point `(2,27)`?

Answer 1

`(x--8)^2=+(50/11)(y-5)" "`Vertex Form

Explanation:

From the given: Vertex (-8, 5) and passing thru (2, 27), the parabola opens upward. The reason is that the vertex is lower than the given point.

By the vertex form , we can solve for the value of `p`

`(x-h)^2=+4p(y-k)`

`(2--8)^2=+4p(27-5)`

`10^2=4p(22)`

`100=4(22)p`

`25=22p`

`p=25/22`

Go back to the vertex form

`(x--8)^2=+4(25/22)(y-5)`

`(x--8)^2=+2(25/11)(y-5)`

`(x--8)^2=+(50/11)(y-5)" "`Vertex Form

graph{(x--8)^2=(50/11)(y-5)[-50,50,-25,25]}

God bless....I hope the explanation is useful.