Question

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)?

Answer 1

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:

$y=a\mleft(x-h\mright)^2+k$

Thus,

$y=a\mleft(x-6\mright)^2-7\ldots(1)$

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,

$\begin{gathered} -9=a\mleft(4-6\mright)^2-7 \\ -9=a(-2)^2-7 \\ -9=4a-7 \\ -9+7=4a \\ -2=4a \\ a=-\frac{2}{4} \\ a=-\frac{1}{2} \end{gathered}$

Thus, subsitute in the equation (1) to get the quadratic equation,

$y=-\frac{1}{2}\mleft(x-6\mright)^2-7$