Regina has finished writing her first book, Successful Steps to

Regina has finished writing her first book, Successful Steps to College Success. She wants to determine the price at which she should sell her book in order to maximize her revenue. This situation is expressed by the equation y=−0.5x2+24x, where x represents the price and y represents the revenue. In terms of the context, what price should Regina sell the book to earn maximum revenue?(1 point)Responses$24$24$288$288$12$12$48

1 answer

To find the price that maximizes Regina's revenue, we need to determine the vertex of the downward-opening parabola represented by the equation $ y = -0.5x^2 + 24x $. The x-coordinate of the vertex of a parabola given by the equation $ y = ax^2 + bx + c $ can be found using the formula:

\[ x = -\frac{b}{2a} \]

In this equation:

$ a = -0.5 $
$ b = 24 $

Substituting these values into the formula gives us:

\[ x = -\frac{24}{2 \times -0.5} = -\frac{24}{-1} = 24 \]

Therefore, the price at which Regina should sell her book to earn maximum revenue is $24.