Question

Write a quadratic function whose graph passes through (3,6) and has the vertex (-2,4) what is the value of Y

Answer 1

The representation of a quadratic eqauation in vertex form is

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

The given vertex is,

`(k,h)=(-2,4)`

And the given point through which the graph passes is,

`(x,y)=(3,6)`

Substitute the values in the formula of quadratic equation.

`\begin{gathered} 6=a(3-(-2))+4 \\ 6=a(3+2)+4 \\ 6=5a+4 \\ 5a=6-4 \\ 5a=2 \\ a=(5)/(2) \end{gathered}`

Hence, the equation in vertex form will be,

`\begin{gathered} y=(5)/(2)(x-(-2))+4 \\ y=(5)/(2)(x+2)+4 \end{gathered}`