Final answer:
To find the maximum of the quadratic function f(x) = -2x² + 8x - 1, calculate the vertex (-b/(2a)). Since it opens downward, it has a maximum at (2, 7).
Step-by-step explanation:
The correct answer is to find the minimum or maximum of the quadratic function f(x) = -2x² + 8x - 1 by completing the square or using the vertex form. Since the coefficient of x² is negative, the quadratic function opens downwards, which means it has a maximum point. The vertex of the quadratic function can be found using the formula -b/(2a) for the x-coordinate of the vertex, where a is the coefficient of x² and b is the coefficient of x.
The x-coordinate of the vertex is x = -b/(2a) = -8/(2*(-2)) = 2. To find the y-coordinate of the vertex, we substitute x back into the function, f(2) = -2(2)² + 8(2) - 1 = -8 + 16 - 1 = 7. Therefore, the maximum point of the quadratic function is (2, 7), and its coordinates are (2,7).
To find the minimum or maximum of a quadratic function, we can use the vertex formula. For a quadratic function in the form of f(x) = ax² + bx + c, the x-coordinate of the vertex is given by x = -b/2a. Plugging in the values from the equation f(x) = -2x² + 8x - 1, we find that x = -8/-4 = 2. Substituting this value back into the function, we get f(2) = -2(2)² + 8(2) - 1 = -8 + 16 - 1 = 7. Therefore, the minimum or maximum point is (2, 7), and it is a maximum as the coefficient of the squared term is negative.