Find an equation for the conic section with the given properties.

Question

Find an equation for the conic section with the given properties.

The parabola that passes through the point (8, −2), with vertex V(5, −1) and vertical axis of symmetry

Answer 1

A parabola with a vertical line of symmetry means the equation fits the form y = x² with the associated "vertex form" being:

y = a(x - h)² + k where the vertex is (h, k) so, for this problem, that would make it:

y = a(x - 5)² - 1

Since the point (8, -2) is on the curve, we can plug it in as an "x" and "y" like this:

-2 = a(8 - 5)² - 1

-1 = 9a

a = -1/9

So the equation is:

y = -1/9(x - 5)² - 1