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)

Question

Responses

$48
$48

$24
$24

$288
$288

$12

Answer 1

To find the price that maximizes Regina's revenue, we need to determine the vertex of the quadratic equation given by \( y = -0.5x^2 + 24x \).

The vertex \( x \) of a parabola described by the equation \( y = ax^2 + bx + c \) can be found using the formula: \[ x = -\frac{b}{2a} \] In this case, \( a = -0.5 \) and \( b = 24 \).

Plugging in these values: \[ x = -\frac{24}{2 \times -0.5} = -\frac{24}{-1} = 24 \]

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

The correct response is: $24