Part 4 of 4 Consider the function \( f(x)=-2 x^{2}+16 x-9 \). a. Determine, without graphing, whether the function has a minimum value or a maximum value. b. Find the minimum or maximum value and determine where it occurs. c. Identify the function's domain and its range. a. The function has a maximum value. b. The minimum/maximum value is 23 . It occurs at \( x=4 \). c. The domain of \( f \) is \( (-\infty, \infty) \). (Type your answer in interval notation.) The range of \( f \) is \( \square \). (Type your answer in interval notation.) The

Quadratic functions like \( f(x) = -2x^2 + 16x - 9 \) can be incredibly interesting because they describe everything from projectile motion to economics. Since the coefficient of \( x^2 \) is negative, the parabola opens downward, indicating that we have a maximum value. This max value is found at the vertex, which can be calculated using the vertex formula \( x = -\frac{b}{2a} \). When it comes to the domain and range, quadratic functions are particularly generous! The domain is always all real numbers \((-\infty, \infty)\). For the range, since we found that the maximum value is 23, that means the function can take on any value less than or equal to 23. Thus, the range is \((-\infty, 23]\).