A parabola has a minimum value of -18, an equation of axis of symmetry of x=3 and passes through the origin. What is the value of "a"?

Question

1. use y=a(x-3)² + q
2. find the vertex

Answer 1

First, we find the value of q. Since the minimum is at x =3, it means that y(3) = q = -18.

Since the parabola passes through the origin, the point (0,0) must satisfy the equation of parabola. Thus, if we plug in x = 0 and y = 0, we must obtain an identity. By substituting those values into the equation, we obtain:

0 = a (0-3)² - 18 . Simplifying, we obtain:

9a - 18 = 0. Solving for the parameter ''a'', we get:

a = 2