Write a cubic function that passes through the points (-3,0), (0,0), (1,-8), and (2,0)

Answer 1

you have 3 zeros, -3, 0 and 2

make them factors, by changing the sign of the zero and stick an x in front of each. then multiply them together

(x+3)(x-0)(x-2) = (x^2 +x -6)x = x^3 +x^2 -6x

f(x) = a(x^3+x^2 -6x) plug in the 4th point (1,-8)to solve for a

-8 = a(4(1)(-1)

a = --8/-4 = 2

f(x) =2x^3 +2x^2 -12x