Find the standard form????????????

Find the standard form of the equation of the parabola with the given characteristics.
Vertex: (8, -5); focus: (8, -3)


thanks

Since the vertex is lower on the y axis than the focus, and x is the same for both the vertex and the focus, we know that the parabola matches the formula x^2 = 4py. Since we are not at the origin with it, we need to do a little work with our x and y variables to get it in line.

Since we are shifted right 8, we need to shift the equation left 8 for x, so instead of x^2 we use (x - 8)^2. Since we are shifted down 5 on the y axis, we substitute (y + 5) for y, and we have our equation.

(x - 8)^2 = 4(-3)(y + 5)

or

(x - 8)^2 = -12(y + 5)

or

(x - 8)^2 = -12y - 60

Really? Sorry about that.

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