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 \\ (8)/(16)=(16a)/(16) \\ (1)/(2)=a \\ \therefore a=(1)/(2) \end{gathered}`

Hence,

`a=(1)/(2)`