Chapter 3 - Polynomial and Rational Functions - 3.1 Quadratic Functions and Models - 3.1 Execises - Page 315: 50

$f(x)=3(x+1)^2-12$

Step 1. Assume the quadratic has a standard form $f(x)=a(x-h)^2+k$ Step 2. Given vertex at $(-1,-12)$, we have $h=-1, k=-12$, thus $f(x)=a(x+1)^2-12$ Step 3. As $(1,0)$ is on the parabola, we have $0=a(1+1)^2-12$ which gives $a=3$ Step 4. We conclude that the function is $f(x)=3(x+1)^2-12$