Question

What are the vertex, focus, and directrix of the parabola with the given equation? see image

Answer 1

Given a parabola written in the form

`y=(1)/(4p)(x-h)^2+k`

The vertex is (h, k), the focus is (h, k+p) and the directrix is y = k - p.

Our parabola equation is

`y=(1)/(28)(x-4)^2-5=(1)/(4\cdot(7))(x-4)^2-5`

Therefore, if we compare with the form presented, the vertex of this parabola is

`(4,-5)`

The focus is

`(4,-5+7)=(4,2)`

And the directrix is

`\begin{gathered} y=-5-7=-12 \\ y=-12 \end{gathered}`