To find the number of rows in the auditorium, we need to solve the equation f(x) = 416.
2x^2 - 6x = 416
2x^2 - 6x - 416 = 0
Now, we need to factor this polynomial or use the quadratic formula to solve for x. Factoring, we get:
2(x^2 - 3x - 208) = 0
2(x - 16)(x + 13) = 0
Setting each factor to zero:
x - 16 = 0
x = 16
x + 13 = 0
x = -13
Since the number of rows cannot be negative, the correct solution is x = 16. Therefore, there are 16 rows in the auditorium.
The 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?
1 answer
1 answer