Chapter 5 Polynomials and Polynomial Functions - 5.7 Apply the Fundamental Theorem of Algebra - 5.7 Exercises - Mixed Review - Page 386: 77

$y=-2 (x+5)(x+1)$

Here, we find the x-intercepts are $-5$ and $-1$. Thus, the function is: $y=a (x+5)(x+1)$ Since $(-2,6)$ is on the graph of this function, we have $6=a (-2+5)(-2+1)$ This gives: $6=3a \implies a=-2$ Hence, the required function is: $y=-2 (x+5)(x+1)$