$a)$

$W=\left(-3,0\right)\Rightarrow f\left(x\right)=a{\left(x+3\right)}^2+0=a{\left(x+3\right)}^2$

$A=\left(-8,15\right)\Rightarrow f\left(-8\right)=15\Rightarrow a\cdot {\left(-8+3\right)}^2=15\Rightarrow 25a=15\Rightarrow a=\frac{15}{25}=\frac{3}{5}$

$\underline{\underline{f\left(x\right)=\frac{3}{5}{\left(x+3\right)}^2}}$