For what value of x will the function f(x) = -3(x - 10)(x - 4) have a maximum value? Find the maximum value.?

Answer 1

this is just a parabola. Its axis of symmetry is midway between the roots.
Naturally, the vertex (maximum y) lies on that axis of symmetry.
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Answer 2

F(x) = -3(x-10)(x-4) = -3(x^2-4x-10x+40) = -3(x^2-14x+40),
F(x) = -3x^2+42x-120.

h = Xv = -B/2A = -42/-6 = 7.
k = Yv = -3*7^2 + 42*7 - 120 = 27.
V(h, k) = V(7, 27). = max point.
So X = 7 at max. point.