Question

Writing Polynomial Function Given a y-Intercept

Answer 1

We already got

f(x)= a(x-2)(x-3)(x-5)

We got $a=\frac{1}{6}$

first we multiply the parenthesis in f(x)

f(x)= a(x-2)(x-3)(x-5)

$f(x)= a(x^2-5x+6)(x-5)$

$f(x) = a(x^3 - 10 x^2 + 31 x - 30)$

Replace the value of 'a'

$f(x) = \frac{1}{6}(x^3 - 10 x^2 + 31 x - 30)$

Multiply 1/16 inside the parenthesis

$f(x) = \frac{1}{6}x^3 - \frac{5}{3} x^2 + \frac{31}{6} x - 5$