Final answer:
The maximum or minimum of the quadratic function is (1, 4) minimum.
Step-by-step explanation:
To find the maximum or minimum of a quadratic function, we need to determine the vertex of the parabola represented by the function. The vertex form of a quadratic function is f(x) = a(x-h)^2 + k, where (h, k) represents the coordinates of the vertex.In this case, the quadratic function is f(x) = -3x^2 + 6x + 1. To find the vertex, we can use the formula -b/2a to find the x-coordinate of the vertex. Plugging in the values of a = -3 and b = 6, we get -6/(2*-3) = 1.Substituting x = 1 back into the original function, we get f(1) = -3(1)^2 + 6(1) + 1 = 4. Therefore, the vertex of the parabola is (1, 4) which represents the minimum point of the function.