Chapter 3 - Polynomial and Rational Functions - 3.1 Quadratic Functions and Models - 3.1 Execises - Page 319: 80

$-2x^2-2x+4$

Step 1. Assume the quadratic function has the form $f(x)=a(x-x_1)(x-x_2)$ Step 2. Given the two x-intercepts, we have $x_1=1, x_2=-2$ Step 3. Given the y-intercept, we have $f(0)=4$ or $a(0-1)(0+2)=4$ which gives $a=-2$ Step 4. Thus the function is $f(x)=-2(x-1)(x+2)=-2x^2-2x+4$