Given : the vertex of the quadratic function = ( -5, -1)
The function passes through (-2,2)
The vertex form is:
[tex]f(x)=y=a(x-h)^2+k[/tex]given:
[tex]\begin{gathered} h=-5 \\ k=-1 \\ x=-2 \\ y=2 \end{gathered}[/tex]Substitute to find a:
[tex]\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}[/tex]So, the vertex form will be:
[tex]f(x)=\frac{1}{3}(x+5)^2-1[/tex]The standard form will be:
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