Write the equation for the parabola given the following information: Vertex (2,2) Directrix at x= -15​

Since the directrix is the vertical line x=4, the axis of the parabola is the horizontal line containing the focus.

So, the axis is the horizontal line y = 0 (the x-axis).

The vertex is on the axis and lies halfway between the focus and directrix.  So, the vertex is (0,0)

Equation of parabola:  (y-0)2 = 4p(x-0).

p is the directed distance between the vertex and focus (since the focus is to the left of the vertex, p < 0.

So, p = -4.   Note:  had the focus been to the right of the vertex, then p would have been positive.  

Equation of parabola:  (y-0)2 = -16(x-0).  Simplify to get y2 = -16x.  

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