7. Let \( f(x) \) be a quadratic function. Discuss how to determine the maximum or minimum value of \( f(x) \).

To determine the maximum or minimum value of a quadratic function \( f(x) = ax^2 + bx + c \), you first look at the coefficient \( a \). If \( a > 0 \), the parabola opens upwards, meaning the function has a minimum value at its vertex. If \( a < 0 \), it opens downwards, indicating a maximum value. The vertex can be found using the formula \( x = -\frac{b}{2a} \). Plug this \( x \) value back into \( f(x) \) to find the corresponding maximum or minimum value. To visualize this, think of a ball rolling down a hill. If the hill is shaped like a smile (U-shaped), the ball will settle at the lowest point (minimum). Conversely, if it’s shaped like a frown (inverted U-shaped), the ball will roll to the highest point (maximum). Use this imagery to help you remember the relationship between the direction of the parabola and the nature of its extremum!