Chapter 5 Polynomials and Polynomial Functions - 5.9 Write Polynomial Functions and Models - 5.9 Exercises - Quiz for Lessons 5.7-5.9 - Page 399: 12

$f(x)=2(x+1)(x-2)(x-4)$

If the function has x-intercepts $a,b,c$, then it has the form $f(x)=k(x-a)(x-b)(x-c)$. Here the x-intercepts are $1,2,4$; hence $f(x)=k(x+1)(x-2)(x-4)$. The function also goes through $(0,16)$; hence: $16=k(1)(-2)(-4)=8k\\k=2$ Hence, the function is $f(x)=2(x+1)(x-2)(x-4)$