Find an equation for the conic section with the given properties. The parabola that passes through the point (8, −2), with vertex V(4, −1) and vertical axis of symmetry

Answer 1

Vertical parabola with vertex V(4, -1) looking like this: (x - 4)² = 4p(y + 1). To get p we have point (8, - 2) on parabola, so (8 - 4)² = 4p(- 2 + 1), 16 = - 4p, p = - 4.

Equation of parabola (x - 4)² = - 16(y + 1)