Answer the questions below about the quadratic function. \[ f(x)=-x^{2}-6 x-10 \] Does the function have a minimum or maximum value? Minimum Maximum What is the function's minimum or maximum value? \( \square \) Where does the minimum or maximum value occur? D

The function is given by f(x) = -x² - 6x - 10. Since the coefficient of x² is -1 (which is less than 0), the parabola opens downward. This means the function attains a maximum value rather than a minimum value. To find the vertex (which gives the maximum point for a downward-opening parabola), use the formula for the x-coordinate of the vertex:   x = -b/(2a) Here, a = -1 and b = -6, so:   x = -(-6) / (2 * -1) = 6 / -2 = -3 Now, compute the maximum value by evaluating f(-3):   f(-3) = -(-3)² - 6(-3) - 10      = -9 + 18 - 10      = -1 Thus: 1. Does the function have a minimum or maximum value?   Maximum 2. The function's maximum value is:   -1 3. This maximum value occurs at:   x = -3 So, the maximum value of -1 occurs when x = -3.