Factored form

Question

The Darien High School play brought in $5400 last year. This year the drama teacher
intends to raise the $6.00 ticket price. Through surveys, it is estimated that for each
$0.25 increase in price, 15 fewer people will come to the play.
Let x represent the number of $0.25 increases in price, and let y represent the total
income.
1.) Write an equation for the quadratic function to represent this relationship in:
a.) factored form

Answer 1

$5400/$6=900 people

(6+0.25x)(900-15x)=y

 

solving...

5400+225x-90x-3.75x^2=y

-3.75x^2+135x+5400=y

this is a parabola opening downward so it has a maximum point at (h,k)

h=-b/2a

h=-135/2(-3.75)

h=-135/(-7.5)

h=1350/75

h=18

there should be 18 $0.25 increases to maximize income

(6+18*$0.25)(900-15*18)

(6+4.5)(900-270)

$10.50*630=$6615 maximum revenue