find the vertex of f(x)=-x^2+3x-2
The general form of the equation is y = ax^2 + bx + c
This is the formula for a parabola; the x coordinate of the
vertex is (-b/2a); the y coordinate is (- (b^2 - 4ac)/4a)
f(x) = -x^2 + 3x - 2
a = -1, b = 3, c = -2
x = -3 / (2 * -1) = -3 / -2 = 1.5
y = - (3^2 - (4 * -1 * -2) / (4 * -1))
y = - (9 - 8) / -4
y = -1 / -4 = 0.25
The vertex is (1.5, 0.25)