The vertex form of a quadratic equation is given by the following expression:
[tex]y=a(x-h)_{}^2_{}+k[/tex]Where "a" is the constant multiplying the term of second order for the quadratic equation and (h,k) are the coordinates of the vertex. Looking on the graph we can determine the vertex to be on the coordinates (-3, -5), therefore:
[tex]\begin{gathered} y=a\lbrack x-(-3)\rbrack^2-5 \\ y=\frac{1}{2}(x+3)^2-5 \end{gathered}[/tex]The correct answer is the third option.
