Final answer:
The function f(x) = -2x^2 + 6x - 3 opens downwards and has a maximum value. This is because the coefficient of the x^2 term is negative. The maximum value can be found by locating the vertex of the parabola.
Step-by-step explanation:
The graph of the function f(x) = -2x^2 + 6x - 3 opens downwards because the coefficient of the x2 term, which is -2, is negative. This indicates that the function has a maximum value rather than a minimum. To determine the maximum value, we can complete the square or find the vertex of the parabola, since the vertex represents the highest point on the graph when the parabola opens downward. In this case, the vertex can be found using the formula -b/(2a) for the x-coordinate and then evaluating f(x) at that x-value to find the maximum y-value.