Final answer:
The vertex of the graph of the quadratic equation f(x) = -2x^2 + 12x - 20 is found using the formula h = -b/(2a), resulting in the vertex at the point (3, 2).
Step-by-step explanation:
The vertex of the quadratic equation f(x) = -2x^2 + 12x - 20 can be found by using the vertex formula h = -b/(2a), where a and b are coefficients from the quadratic equation in the standard form ax^2 + bx + c. In this case, a is -2 and b is 12, so the x-coordinate of the vertex is h = -12/(2*(-2)) = 3. To find the y-coordinate of the vertex, we substitute x with 3 into the equation, yielding f(3) = -2(3)^2 + 12(3) - 20 = 2. Thus, the vertex of the graph is at the point (3, 2).