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:

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

So, the vertex form will be:

$f(x)=\frac{1}{3}(x+5)^2-1$

The standard form will be:

$undefined$