Answer-
The general form of the equation of the quadratic function is,
[tex]\Rightarrow y= (x+6)^2 -1[/tex]
Solution-
General vertex form of a quadratic,
[tex]y = a(x - h)^2 + k[/tex]
Where,
a = focus,
h = x-coordinate of vertex,
k = y-coordinate of vertex.
As the point (−9, 8) lies on the curve, so it must satisfy the curve equation.
[tex]\Rightarrow 8 = a(-9 - (-6))^2 + (-1)[/tex]
[tex]\Rightarrow 8 = a(-3)^2 -1[/tex]
[tex]\Rightarrow 8 = 9a -1[/tex]
[tex]\Rightarrow 9 = 9a[/tex]
[tex]\Rightarrow a=1[/tex]
∴ Then the equation becomes,
[tex]\Rightarrow y= 1(x- (-6))^2 + (-1)[/tex]
[tex]\Rightarrow y= (x+6)^2 -1[/tex]
