Given:
[tex]\begin{gathered} Vertex:(h,k)=(3,4) \\ Point:(x,y)=(7,12) \end{gathered}[/tex]
The equation given is,
[tex]y=a(x-h)^2+k[/tex]
Therefore,
[tex]\begin{gathered} 12=a(7-3)^2+4 \\ 12=a(4)^2+4 \\ 12=16a+4 \\ 12-4=16a \\ 8=16a \\ \frac{8}{16}=\frac{16a}{16} \\ \frac{1}{2}=a \\ \therefore a=\frac{1}{2} \end{gathered}[/tex]
Hence,
[tex]a=\frac{1}{2}[/tex]
