Question

1. The total number of seats in an auditorium is modeled by f(x) = 2x2 – 6x, where x represents the number of rows. How many rows are there in the auditorium if it has a total of 416 seats? Jose knows to plug in the total seats for f(x): 416 = 2x2 – 6x

Jose needs to solve for x to determine the number of rows. He decides to use his calculator. Under y =, he types in 2x2 – 6x. He checks the table for when y = 0.
He gets the two solutions:
x = 0, x= 3
Jose determines the auditorium has 3 rows.



Error:


Correct solution:

Answer 1

Jose's solution is not correct, the auditorium has
`16` rows

Explanation:

we have

`f(x)=2x^(2) -6x`

where

f(x)------> is the total number of seats in an auditorium

x----> represents the number of rows

How many rows are there in the auditorium if it has a total of 416 seats?

Find the value of x for f(x)=416 seats

substitute the value of f(x) in the equation

`416=2x^(2) -6x`

`2x^(2) -6x-416=0`

Using a graphing calculator

The values of x are
`x=-13, x=16`

The solution is

x=16 rows because the number of rows can not be a negative number