Chapter 5 Polynomials and Polynomial Functions - 5.7 Apply the Fundamental Theorem of Algebra - 5.7 Exercises - Mixed Review - Page 386: 76

$y=\dfrac{1}{2} (x+2)(x-4)$

Here, we find the x-intercepts are $-2$ and $4$. Thus, the function is: $y=a (x+2)(x-4)$ Since, $(2,-4)$ is on the graph of this function, we have $-4=a (2+2)(2-4)$ This gives: $-4=-8a \implies a=\dfrac{1}{2}$ Hence, the required function is: $y=\dfrac{1}{2} (x+2)(x-4)$