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

$y=\frac{1}{4p}(x-h)^2+k$

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

Our parabola equation is

$y=\frac{1}{28}(x-4)^2-5=\frac{1}{4\cdot(7)}(x-4)^2-5$

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

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