Q:

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 – 6xJose 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= 3Jose determines the auditorium has 3 rows. Error:Correct solution:

Accepted Solution

A:
Answer:Jose's solution is not correct, the auditorium has [tex]16[/tex] rowsStep-by-step explanation:we have[tex]f(x)=2x^{2} -6x[/tex]wheref(x)------> is the total number of seats in an auditoriumx----> 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 seatssubstitute the value of f(x) in the equation[tex]416=2x^{2} -6x[/tex][tex]2x^{2} -6x-416=0[/tex]Using a graphing calculatorThe values of x are [tex]x=-13, x=16[/tex]The solution isx=16 rows because the number of rows can not be a negative number