What is the equation of the quadratic function with roots -2 and 4 and a vertex at (1,9)

If the quadratic function has roots -2 and 4, we can write
f(x) = (x - (-2))(x - 4)

=> f(x) = (x + 2)(x -
4)

=> f(x) = x^2 - 4x + 2x -
8

=> f(x) = x^2 - 2x -
8

The vertex of the function is the minimum point. This is
given at the point where f'(x) = 0

=> 2x - 2 =
0

=> x = 1

f(1) = 1 - 2
- 8 = -9

The vertex for the function is (1,
-9).

For the given roots the quadratic function that we
arrive at has the vertex at (1, -9), not
(1,9)

The quadratic function with roots -2
and 4 is f(x) = x^2 - 2x - 8.