What are the factors of the function represented by this graph?

In factor form this is -1/4(x + 4)(x - 8).

Step-by-step explanation:

It has a maximum so the coefficient of x^2 is negative and i  also has 2 factors

( x + 4)(x - 8) , because of the 2 zeroes -4 and 8.

The equation is  y = -a(x + 4)(x - 8) where a is some constant.

The vertex is at (2, 9) so substituting we have:

9 = -a(2 + 4)(2 - 8)

-36* -a = 9

a = 9/36 = 1/4.

So the function is -1/4(x + 4)(x - 8).