Final answer:
To find the maximum of the quadratic function f(x) = 8 - x² + 4x, we rewrite it in vertex form to determine the vertex. Since the coefficient of x² is negative, the function has a maximum at the vertex. The maximum point of the function is at the coordinates (2, 12).
Step-by-step explanation:
The task is to find the maximum or minimum of a quadratic function, which is given by the equation f(x) = 8 - x² + 4x. Since the coefficient of the x² term is negative, the parabola opens downwards, and therefore the function has a maximum point.
To determine the coordinates of this maximum, we can complete the square or use the vertex form of a quadratic function, which is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. The quadratic function f(x) can be rewritten as:
f(x) = -(x² - 4x) + 8
f(x) = -(x² - 4x + 4) + 8 + 4
f(x) = -(x - 2)² + 12
From this, we can see that the vertex (h, k) of the parabola is (2, 12), which is also the maximum point of the function. Therefore, the coordinates of the maximum are (2, 12).