Respuesta :

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]

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