okay the question is in the other part...?

Question

Determine a quadratic function f(x)=ax^2+bx+c if it admits a maximum euqual to 9 and passes though the points (1,-7) and (-1,-27)

Thank you : D

Answer 1

This is a parabola, and in the form:
y - k = P(x - h)^2
The maximum is achieved at y = 9
Plug in the first point to get (1) and the second point to get (2).
(1) -7 - 9 = P(1 - h)^2
P = -16/(1 - h)^2
(2) -27 - 9 = P(-1 - h)^2
P = -36/(-1 - h)^2
Set the two expressions for P equal to each other:
-16/(1 - h)^2 = -36/(-1 - h)^2
4/(1 - h) = 6/(-1 - h)
2(-1 - h) = 3(1 - h)
-2 - 2h = 3 - 3h
h = 5
Plug into (1) to get P:
P = -16/(1 - 5)^2 = -1
So the equation is:
y - 9 = -(x - 5)^2
y = -(x^2 - 10x + 25) +9
y = -x^2 + 10x -16