To find the price that Regina should sell her book in order to maximize her revenue, we can analyze the quadratic revenue function given by:
\[ y = -0.5x^2 + 24x \]
This is a quadratic equation in the form \( y = ax^2 + bx + c \), where:
- \( a = -0.5 \)
- \( b = 24 \)
The vertex of a parabola represented by a quadratic equation \( y = ax^2 + bx + c \) gives the maximum (or minimum) point of the function. Since \( a < 0 \), the parabola opens downwards, and thus the vertex will represent the maximum revenue.
The x-coordinate of the vertex can be calculated using the formula:
\[ x = -\frac{b}{2a} \]
Substituting the values of \( a \) and \( b \):
\[ x = -\frac{24}{2 \cdot -0.5} \] \[ x = -\frac{24}{-1} \] \[ x = 24 \]
Thus, to maximize her revenue, Regina should sell the book at $24. Therefore, the correct response is:
$24