Quadratic equations have the following general form:
[tex]y=ax^2+bx+c[/tex]The general expression for the vertex coordinates is:
[tex](-\frac{b}{2a},-\frac{b^2}{4a}+c)[/tex]Then, when the vertex is (-2,3) we have:
[tex]\begin{gathered} -\frac{b}{2a}=-2 \\ -\frac{b^2}{4a}+c=3 \end{gathered}[/tex]From the first line, we have b = 4a
Then, for a = 1, a = 2 and a = 3, we have three diferent equations:
[tex]undefined[/tex]