How do you determine the equation of a parabola which has a vertex of (0,-4) and has an x-intercept of -3?

Answer 1

Hi Asked, start with the vertex form of the parabola, y = a(x - h)² + k. You are given the h and k values in the vertex of (0, -4). Substitute for h and k gives:

y = a(x - 0)² - 4, or y = ax² - 4

We need to find a. Since it is given there is an x-intercept of -3, solve y = ax² - 4, substituting -3 for x and 0 for y (remember the the point for an x-intercept is (x, 0):

0 = a(-3)² - 4

0 = 9a - 4

9a = 4

a = 4/9

The equation of the parabola with vertex at (0, - 4) and x-intercept at -3 is:

y = 4/9 * x² - 4

Questions?