Step-by-step explanation:
The vertex form of a parabola is given by
[tex]y = a(x - h)^2 + k[/tex]
where (h, k) are the coordinates of the vertex of the parabola. So we can write our parabola as
[tex]y = a(x - 3)^2 + 3[/tex]
We know that our curve goes through the point (2, -1) so we can solve for the constant a as follows:
[tex]-1 = a(2 - 3)^2 + 3 \Rightarrow -1 = a + 3[/tex]
or
[tex]a = -4[/tex]
Therefore, the vertex form of the equation for the parabola is
[tex]y = -4(x - 3)^2 + 3[/tex]
