F(x) = 2x ^2 - 6x the total number of seats in an auditorium is modeled by the function f(x), 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? a) 32 b) 13 c) 20 d) 16

The given function is

Here represents the number of rows.

represents the total number of seats in the auditorium.

Now the total seats in the auditorium are 416.

So

Dividing all terms by 2 we get

Subtracting 208 from both sides

Factoring we get

(x-16)(x+13)=0

Using Zero product rule

x - 16= 0 or x+13=0

x= 16 or x = -13

But as x cannot be negative

So x = 16

There are 16 rows in the auditorium if it has a total of 416 seats.

The number of rows will be 16 rows

Given the function that represents the total number of seats in an auditorium as;

If the auditorium has a a total of 416 seats, then;

416 = 2x^2 - 6x

2x^2 - 6x - 416 = 0

x^2 - 3x - 208 = 0

Factorize to get the value of x:

On factorizing, x = -13 and 16

Since x cannot be negative, hence the number of rows will be 16 rows

Learn more on factorization here:link

b

step-by-step explanation: