Find the quadratic function that pass through (-3,0), (1,-6), (5,0)

Answer 1

(-3,0), (1,-6) and (5,0) have a quadratic curve through them. It's a parabola with axis of symmetry x = average of the x intercepts x=(5-3)/2 = 2/2 = 1

vertex is (1,-6)

f(x) = a(x-1)^2 -6 solve for a by plugging in either x intercept

0 = a(5-1)^2 - 6

6 = 16a

a = 6/16 = 3/8

f(x) = (3/8)(x-1)^2 -6 is the quadratic function whose graph includes the 3 given points