Plug $x=5$ into your expression for $f(x)$ and set it equal to $9$ to solve for $a$.

The $y$-intercept of $g$ is $g(0)$. А-n-i‌-k-o​.a​i Carefully substitute $x=0$ into $g(x)=f(x-1)+f(1-x)$.

Enter $f(x)=a(x+4)(x-2)$ and let $a$ be a slider.

Plot the point $(5,9)$. an‌ik‍о.а‌i ⁠S⁠АT Queѕt​i‌οn Ваnk Adjust the slider $a$ until the graph of $y=f(x)$ passes through $(5,9)$.

Enter $g(x)=f(x-1)+f(1-x)$. Then evaluate $g(0)$ (for example, by typing g(0)), which gives the $y$-intercept.

Since the $x$-intercepts are $-4$ and $2$, the function has the form

аnikо⁠.аі

for some constant $a$.

Substitute $x=5$ and $f(5)=9$:

So $a=\frac{1}{3}$, and

The $y$-intercept of $g$ is $g(0)$:

Compute each value:

Then

So the $y$-intercept of $g$ is $-\frac{14}{3}$.