The equation of a quadratic function with roots -2 and 4 is given by:
(x + 2)(x - 4) = 0
x^2 - 4x + 2x - 8 = 0
x^2 - 2x - 8 = 0
f(x) = x^2 - 2x - 8
Since the vertex is at point (1, 9) which is above the roots. This means that the parabola representing the function is facing down and the leading coeficient is negative.
Therefore the function becomes:
f(x) = -(x^2 - 2x - 8)
f(x) = -x^2 + 2x + 8