What is the equation, in vertex form, of the quadratic function that has a vertex at V(6, −7) and passes through point P(4, −9)?

given data:
vertex at V(6, −7)
passes through point P(4, −9).
In general a parabola in vertex(h,k) form can be written as:
[tex]y=a\mleft(x-h\mright)^2+k[/tex]Thus,
[tex]y=a\mleft(x-6\mright)^2-7\ldots(1)[/tex]Since, the point P(4, −9) passes through the parabola,
we can write as follows and solve the equation to find the value of a,
[tex]\begin{gathered} -9=a\mleft(4-6\mright)^2-7 \\ -9=a(-2)^2-7 \\ -9=4a-7 \\ -9+7=4a \\ -2=4a \\ a=-\frac{2}{4} \\ a=-\frac{1}{2} \end{gathered}[/tex]Thus, subsitute in the equation (1) to get the quadratic equation,
[tex]y=-\frac{1}{2}\mleft(x-6\mright)^2-7[/tex]