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

What are the vertex, focus, and directrix of the parabola with the given equation-example-1
User Ian Selby
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1 Answer

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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}

User Ray Doyle
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