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

$288
$288

$24
$24

$12
$12

$48

1 answer

To determine the price at which Regina should sell her book to maximize revenue, we can analyze the quadratic revenue equation given:

\[ y = -0.5x^2 + 24x \]

This is a quadratic equation in the standard form $ y = ax^2 + bx + c $, where $ a = -0.5 $ and $ b = 24 $. The graph of this quadratic function is a downward-opening parabola (since $ a < 0 $), and the maximum revenue occurs at the vertex of the parabola.

The x-coordinate of the vertex of a quadratic equation can be found using the formula:

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

Plugging in the values of $ a $ and $ b $:

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

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

The correct response is $24.