Question

The quadratic Function has a vertex at (3,4). The quadratic also goes through the point (7,12). Find the value using the information.y=a(x-h)^2+k

Answer 1

Given:

$\begin{gathered} Vertex:(h,k)=(3,4) \\ Point:(x,y)=(7,12) \end{gathered}$

The equation given is,

$y=a(x-h)^2+k$

Therefore,

$\begin{gathered} 12=a(7-3)^2+4 \\ 12=a(4)^2+4 \\ 12=16a+4 \\ 12-4=16a \\ 8=16a \\ \frac{8}{16}=\frac{16a}{16} \\ \frac{1}{2}=a \\ \therefore a=\frac{1}{2} \end{gathered}$

Hence,

$a=\frac{1}{2}$