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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

Respuesta :

The given function is

[tex] f(x) = 2x^2 - 6x [/tex]

Here [tex] x [/tex] represents the number of rows.

[tex] f(x) [/tex] represents the total number of seats in the auditorium.

Now the total seats in the auditorium are 416.

So [tex] f(x) = 416 [/tex]

[tex] 2x^2-6x=416 [/tex]

Dividing all terms by 2 we get

[tex] x^2-3x=208 [/tex]

Subtracting 208 from both sides

[tex] x^2-3x-208=0 [/tex]

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.

abidemiokin

The number of rows will be 16 rows

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

  • f(x) = 2x^2 - 6x

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:https://brainly.com/question/25829061

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