Question

The following function represents the profit P(n), in dollars, that a concert promoter makes by selling tickets for n dollars each:

P(n) = -250n2 + 3,250n - 9,000

Part A: What are the zeroes of the above function, and what do they represent? Show your work. (4 points)

Part B: Find the maximum profit by completing the square of the function P(n). Show the steps of your work. (4 points)

Part C: What is the axis of symmetry of the function P(n)? (2 points)

Answer 1

PLEASE HELP ILL MEDAL

Answer 2

by some miracle this factors as
\[-250 (n-4) (n-9)\] so the zeros should be easy to find, solve
\[(n-4)(n-9)=0\]

Answer 3

I already have Part A.

Answer 4

@satellite73

Answer 5

oh find the first coordinate of the max via \(x=-\frac{b}{2a}\)

Answer 6

in your case it is \(\frac{13}{2}\) or \(6.5\)

Answer 7

So thats Part B?

Answer 8

not coincidentally half way between the zeros

Answer 9

to find the second coordinate of the max, evaluate the function at \(\frac{13}{2}\) let me know what you get
then i can show you what it looks like when the square is completed

Answer 10

where would you plug it in?

Answer 11

here \[P(n) = -250n^2 + 3,250n - 9,000\] use a calculator

Answer 12

P(n)=-250(n-4)(n-9)

Answer 13

what is
\[P(\frac{13}{2})\]?

Answer 14

\[\frac{ 13P }{ }\]

Answer 15

over 2
sorry

Answer 16

@satellite73

Answer 17

i sense you are lost
\[P(n)\] is a function
\[P(\frac{13}{2})\] is a number
since
\[P(n) = -250n^2 + 3,250n - 9,000\] then
\[P(\frac{13}{2}= -250(\frac{13}{2})^2 + 3,250(\frac{13}{2}) - 9,000\]

Answer 18

oh okay, so solve the last equation?

Answer 19

@satellite73

Answer 20

solve in this case means compute it
use a calculator

Answer 21

here i will show you an easy on line one to use

Answer 22

http://www.wolframalpha.com/input/?i=-250%2813%2F2%29^2%2B3250%2813%2F2%29-9000

Answer 23

so, that would be Part B?

Answer 24

that means is "vertex form" you have
\[P(n)=-250(n-6.5)^2+1562.5\]

Answer 25

i resorted to decimals because the fractions were getting annoying
and yes, that is the answer to B

Answer 26

okay, what about Part C?

Answer 27

Find the maximum profit by completing the square of the function P(n). Show the steps of your work. (4 points)
the maximum is \(1562.5\) which occurs if \(n=6.5\) and therefore the vertex form is
\[P(n)=-250(n-6.5)^2+1562.5\]
you may notice that i did not actually complete the square, it is easier to find the vertex without doing that

Answer 28

Part C: What is the axis of symmetry of the function P(n)? (2 points)

Answer 29

already found it, it is the first coordinate of the vertex written as a line
\[x=\frac{13}{2}\] or
\[x=6.5\]

Answer 30

13/2?

Answer 31

right

Answer 32

Can you help me on another?

Answer 33

sure if it is quick

Answer 34

Kim is studying the sale of a particular brand of cereals from the year 2000 to 2010. She writes the following function to model the sale of the cereal S(t), in million dollars, after t years:

S(t) = t2 + 7t + 69

Part A: What does the y-intercept of the graph of the function represent? (4 points)

Part B: What is the reasonable domain of the graph of the function? (3 points)

Part C: What is the average rate of change of the sale of the cereal from the first year to the fourth year? Show your work. (3 points)

Answer 35

I already have Part A & B. Just need Part C

Answer 36

\[S(t) = t^2 + 7t + 69\] the y intercept is 69, the millions of dollars when you start, in 2000

Answer 37

oh you got that ok

Answer 38

Part C: What is the average rate of change of the sale of the cereal from the first year to the fourth year? Show your work. (3 points)


this always confuses me
i assume the first year is \(2000\) so the fourth year is \(2003\) then the average rate of change is the slope
\[\frac{s(3)-s(0)}{3-0}\]

Answer 39

Thank you so much!

Answer 40

\[S(t) = t^2 + 7t + 69\]
\[S(0)=69\]
\[S(3)=99\]
\[\frac{S(3)-S(0)}{3}=\frac{99-69}{3}=\frac{30}{3}=10\]

Answer 41

yw