write an equation of a parabola with a vertex at ( 2,-2), opening to the right, and going through the point ( 3, -10)

Question

I know that the standard form for a parabola not centered at the origin is ( x - h)^2 / a^2 + ( y - v)^2/ b^2 = 1

Answer 1

The vertex form of parabola equation is x = a(y - k)² + h, where (h, k) = vertex .

Where, vertex (h, k) = (2, - 2) and the point (x, y) = (3, - 10).

Substitute (h, k) = (2, - 2) and (x, y) = (3, - 10). in vertex form : x = a(y - k)² + h.

3 = a(-10 + 2)² + 2

3 = a(-8)² + 2

3 = 64a + 2

64a = 3 - 2

a = 1/64

Substitute a = 1/64  and (h, k) = (2, - 2) in vertex form.

x = (1/64)(y + 2)² + 2.

Therefore, the parabola equation is x = (1/64)(y + 2)² + 2.