Answer
$y =-0.75 x^2+7.05x -2.7$
Work Step by Step
Since the zeros of the function are located at $x= \frac{2}{5}$ and $x= 9$, we write
$$
\begin{aligned}
f(x) & =a \left(x- \frac{2}{5} \right)\left( x-9\right).
\end{aligned}
$$ Given that $f(4)=13.5$, we can use the point $(x,y) = (4 , 13.5) $ to find the constant $a$. Plug this point into the above equation to find the value of $a$. $$
\begin{aligned}
13.5& =a\left(4- \frac{2}{5} \right)\left( 4-9\right)\\
13.5& = \frac{4\cdot 5-2}{5}(-5)a\\
13.5& = \frac{20-2}{5}(-5)a\\
13.5& = \frac{18}{5}(-5)a\\
13.5& = -18a\\
a&=- \frac{13.5}{18}\\
a& = -0.75.
\end{aligned}
$$ This gives $$
\begin{aligned}
y& =-0.75\left(x- \frac{2}{5} \right)\left( x-9\right)\\
&= -0.75\left[ \left(x- \frac{2}{5} \right)x-\left(x- \frac{2}{5} \right)9 \right]\\
&=-0.75\left[ x^2- 0.4x -9x+ \frac{18}{5}\right]\\
&=-0.75\left[ x^2- 9.4x + 3.6\right]\\
& =-0.75 x^2+7.05x -2.7.
\end{aligned}
$$
