taking a close look at the graph hmmm we can see that it has roots or solutions at -4 and 5, however, let's notice something, the graph touches the x-axis at -4 and 5 but it doesn't cross it, it simply bounces off of it, which means those roots have an even multiplicity, hmmm let's give it say 2. Let's also notice the graph has a y-intercept at hmm 100, so the graph passes through (0 , 100).
[tex]\begin{cases} x=-4\implies &x+4=0\\\\ x=5\implies &x-5=0 \end{cases}\implies y=a\stackrel{"2" multiplicity}{(x+4)^2 (x-5)^2} \\\\\\ \textit{we also know} \begin{cases} x=0\\ y=100 \end{cases}\implies 100=a(0+4)^2 (0+5)^2 \\\\\\ 100=a(16)(25)\implies \implies \cfrac{100}{(16)(25)}=a\implies \cfrac{1}{4}=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=\cfrac{1}{4}(x+4)^2 (x-5)^2~\hfill[/tex]
Check the picture below.
