Question

The total number of seats in an auditorium is modeled by f(x)=2x^(2)-6x, where x represents the number of rows of seats. How many rows are there in the auditorium if it has a total of 416 seats?

Answer 1

To find the number of rows in the auditorium, solve the equation f(x) = 2x^2 - 6x = 416 using the quadratic formula.

Step-by-step explanation:

To find the number of rows in the auditorium, we need to solve the equation f(x) = 2x^2 - 6x = 416. Rearranging the equation gives us 2x^2 - 6x - 416 = 0. Now we can use the quadratic formula to solve for x:

x = (-(-6) ± sqrt((-6)^2 - 4(2)(-416))) / (2(2))

x = (6 ± sqrt(2936)) / 4

Calculating the values, we get x = 17 and x = -12. Since x represents the number of rows, we can ignore the negative value. Therefore, there are 17 rows in the auditorium.