Question

F(x) = 2x ^2 - 6x

Answer 1

The given function is

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

Here $x$ represents the number of rows.

$f(x)$ represents the total number of seats in the auditorium.

Now the total seats in the auditorium are 416.

So $f(x) = 416$

$2x^2-6x=416$

Dividing all terms by 2 we get

$x^2-3x=208$

Subtracting 208 from both sides

$x^2-3x-208=0$

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.