a quadratic function that contains (4,-64) and it’s vertex is at the irgun of (0,0)

Answer 1

The basic equation for a parabola (quadratic function) is f(x) = a(x - h)² + k where the vertex is at the point (h, k). Since the origin (0, 0) is the vertex, we can plug in 0 for h and k so the equation becomes f(x) = a(x - 0)² + 0 or f(x) = ax²

Since we know that (4, -64) is a point on the curve, then f(4) must equal -64 so we can plug in those values for x and y to get -64 = a(4)² then we can solve for a: -64 = 16a or a = -64/16 = -4 so the function is:

f(x) = -4x²