write a function in any form that would match the graph shown below. answer $f(x)=$

Answer:

$f(x)=-(x + 8)(x+2)$

Explanation:

Step1: Identify x - intercepts

The x - intercepts are $x=-8$ and $x = - 2$. So the factored form of the quadratic function is $f(x)=a(x + 8)(x + 2)$.

Step2: Determine the value of a

The parabola opens downwards, so $a<0$. Let's use the y - intercept. When $x = 0$, from the graph $y=-16$. Substitute $x = 0$ and $y=-16$ into $f(x)=a(x + 8)(x + 2)$: $-16=a(0 + 8)(0+2)$, $-16=a\times8\times2$, $-16 = 16a$, so $a=-1$. Then $f(x)=-(x + 8)(x+2)$.