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The directrix and focus of a parabola are shown on the graph. Which is an equation for the parabola?X=-5

The directrix and focus of a parabola are shown on the graph. Which is an equation-example-1

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From the graph, we notice that the parabola has to be a horizontal parabola with vertex at:


(-2,3),

that opens to the right.

Recall that the standard form of a horizontal parabola is:


\mleft(y-k\mright)^2=4p\mleft(x-h\mright)\text{.}

Where, (h,k) are the coordinates of the vertex, and p is the distance to the vertex to focus.

Substituting the vertex in the above equation, we get:


(y-3)^2=4p(x-(-2))\text{.}

From the diagram, we get that:


p=3.

Therefore:


(y-3)^2=12(x+2)\text{.}

Solving the above equation for x, we get:


\begin{gathered} ((y-3)^2)/(12)=x+2, \\ x=((y-3)^2)/(12)-2. \end{gathered}

Answer:


x=((y-3)^2)/(12)-2.

User Ramiromd
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