Question

Find the equation for a polynomial f(x) that satisfies the following:

Degrees 3

Zero at x 4

Zero at x -3

Zero at x -4

Y intercept (0,8)

Answer 1

f(x) = 1/2(4 - x)(x - 1)(x - 2)

Explanation:

Considering zero's and a coefficient, the function is:

f(x) = a(x - 4)(x - 1)(x - 2)

Considering y-intercept:

f(0) = a(0 - 4)(0 - 1)(0 - 2)

4 = a(-4)(-1)(-2)

4 = -8a

a = -1/2

So the function is:

f(x) = -1/2(x - 4)(x - 1)(x - 2) = 1/2(4 - x)(x - 1)(x - 2)