The equation of a parabola can be express as follows
[tex]\begin{gathered} y=a(x-p)(x-q) \\ y=a(x+3)(x-5) \\ x=4 \\ y=-21 \\ -21=a(4+3)(4-5) \\ -21=a\times7\times-1 \\ -21=-7a \\ a=3 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} substitute\text{ for a} \\ y=a(x-p)(x-q) \\ y=3(x+3)(x-5) \end{gathered}[/tex]