Final answer:
The function f(x) = -(x-3)^2 + 49 is a quadratic function that opens downward with a positive leading coefficient.
Step-by-step explanation:
The general form of a quadratic function is f(x) = ax^2 + bx + c.
The function f(x) = -(x-3)^2 + 49 is a quadratic function. In this case, a = -1, b = 6, and c = 49.
At x = 3, the function has a positive value, which means the vertex of the parabola is above the x-axis.
The positive slope that is decreasing in magnitude with increasing x indicates that the parabola opens downward.