Question

I just need the vertex and standard form

Answer 1

Given : the vertex of the quadratic function = ( -5, -1)

The function passes through (-2,2)

The vertex form is:

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

given:

`\begin{gathered} h=-5 \\ k=-1 \\ x=-2 \\ y=2 \end{gathered}`

Substitute to find a:

`\begin{gathered} 2=a\cdot(-2+5)^2+(-1) \\ 2=9a-1 \\ 2+1=9a \\ 3=9a \\ a=(3)/(9)=(1)/(3) \end{gathered}`

So, the vertex form will be:

`f(x)=(1)/(3)(x+5)^2-1`

The standard form will be: