Chapter 5 Polynomials and Polynomial Functions - 5.9 Write Polynomial Functions and Models - Guided Practice for Examples 1 and 2 - Page 394: 1

$f(x)=0.25(x+4)(x-2)(x-5)$

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 $-4,2,5$, hence $f(x)=k(x+4)(x-2)(x-5)$. The function also goes through $(0,10)$, hence: $10=k(4)(-2)(-5)=40k\\k=0.25$ Hence $f(x)=0.25(x+4)(x-2)(x-5)$