Question

Assume that the equation A = −125x²+6x+5.257 models the attendance of a recently released movie where x is the number of weeks since the release and A is the attendance in millions. During what week will the movie attain the highest attendance?

Answer 1

The movie will reach the highest attendance during week 0, indicating that peak attendance occurs at the time of release. This result is calculated by finding the vertex of the quadratic equation modeling attendance over time.

Step-by-step explanation:

To determine when the movie will attain the highest attendance, we need to find the vertex of the quadratic equation A = −125x²+6x+5.257 which models attendance over time. A quadratic function of the form ax² + bx + c will have its vertex at the x-value x = -b/(2a). In this case, the values for a and b are -125 and 6 respectively.

To calculate the x-value for the vertex:

x = -b/(2a)

x = -6/(2*(-125))

x = -6/(-250)

x = 0.024

Since the context of the problem is measured in whole weeks, we would round to the nearest whole week. Therefore, the movie will attain the highest attendance during week 0, which implies the peak attendance occurs when the movie is released.