Determine a polynomial equation for a graph that passes through the point (6, -196) and has three x-intercepts at (-8, 0), (-1, 0), and (5, 0).

Question

I need to show my work.

Answer 1

f(x) = a(x+8)(x+1)(x-5)

f(6) = -196 = a(6+8)(6+1)(6-5) = a(14)(7) = 91a

91a = -196

a =-196/91

f(x) = (-196/91)(x+8)(x+1)(x-5) or

y=(-196)/91)(x+8)(x+1)(x-5) or

91y =-196(x+8)(x+1)(x-5)

91y =-196(x^2+9x+8)(x-5)

91 =-196(x^3 +4x^2 -37x -40)

91 =-196x^3 - 784x^2 + 7252x + 7840

196x^3 + 784x^2 -7252x - 7749 = 0 has the 3 given zeros & f(6)=-196