SOLUTION: Write the equation of the parabola that has the given charcteristics. Vertex(3,-2) directris x=-5

Question 1143056: Write the equation of the parabola that has the given charcteristics.
Vertex(3,-2) directris x=-5
Answer by greenestamps(13215) (Show Source): You can put this solution on YOUR website!
The directrix is vertical (x=-5); the vertex is to the right of the directrix. So the parabola opens to the right.

The vertex form of the equation is

where the vertex is (h,k) and p is the directed distance from the directrix to the vertex and from the vertex to the focus.

The given information allows us to write the equation with just one simple calculation.

The vertex (h,k) is (3,-2); and p is the directed distance from the directrix to the vertex -- i.e., the directed distance from -5 to 3 -- so p=8. Then the equation is

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