The equation of the parabola is y = -1/9(x- 1)^2 - 6.
If a quadratic equation is written in the form
y=a(x-h)^2 + k
then it is called to be in vertex form.
It is given that the equation passes through (4 -7) and has vertex (1 -6) in vertex form will be;
y=a(x-h)^2 + k
Since the vertex is at (1, -6), we can write the equation as
y = a(x- 1)^2 - 6
Also, since the parabola passes through (4, -7), we can find the value for a,
-7 = a(4 - 1)^2 - 6
-7 = 9a - 6
a = -1/9
Hence, the equation of the parabola is
y = -1/9(x- 1)^2 - 6
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