👉 To solve this problem, we first need to define the objective, which is likely to find the maximum value of a function. Let's assume we're dealing with a simple optimization problem where we want to maximize a quadratic function, such as \(f(x) = -2x^2 + 8x + 3\). This function is a parabola opening downwards (since the coefficient of \(x^2\) is negative), meaning it has a maximum point at its vertex. The x-coordinate of the vertex can be found using the formula \(x = -\frac{b}{2a}\), where \(a\) and \(b\) are coefficients from the quadratic equation \(ax^2 + bx + c\). Here, \(a = -2\) and \(b = 8\), so \(x = -\frac{8}{2(-2)} = 2\). To find the maximum value, we substitute \(x = 2\) back into the function: \(f(2) = -2(2)^2 + 8(2) + 3 = -8 + 16 + 3 = 11\). Therefore, the maximum value of the function is 11, occurring at \(x = 2\).
