From the figure we notice that this graph is a vertical parabola. We know that the equation of a parabola of this kind is
[tex]y=a(x-h)^2+k[/tex]
where (h,k) is the coordinate of the vertex of the parabola.
From the figure we know that the vertex is the point (2,-3) but we don't know the value of a yet. To find the value of a we notice that the parabola passes through the point (3,-2); this means that in this point x=3 and y=-2.
Using this values in the equation above we have an equation for a.
[tex]\begin{gathered} -2=a(3-2)^2-3 \\ -2+3=a(1)^2 \\ a=1 \end{gathered}[/tex]
Therefore, the equation of the parabola described in the graph is
[tex]y=(x-2)^2-3[/tex]
