FAN AND MEDAL
The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, being sold by the company:
graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 6, 0. The vertex is at 3, 120
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit?
Part B: What is an approximate average rate of change of the graph from x = 3 to x = 5, and what does this rate represent?

- anonymous

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- anonymous

##### 1 Attachment

- anonymous

@triciaal yayy!!

- anonymous

do you know how to do this?

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## More answers

- triciaal

the x-intercept means y = 0
f(x) = 0 f(x) = profit
maximum value = highest y value = highest profit

- anonymous

so x-intercept means theres 0 profit?

- triciaal

vertex is at 3, 120 so when x = 3 y = 120
3 pens maximum profit $120

- triciaal

yes

- anonymous

ok and what about the increasing intervals?

- triciaal

question is asking how does y change as x changes

- anonymous

the more pens sold the higher the profit?

- anonymous

but aren't they asking for the intervals where the function is increasing and decreasing

- triciaal

up to the limit of 3 maximum
so x 0 to 3 increase

- triciaal

x more than 3 profit decrease

- anonymous

x more than 3 profit decrease ?

- triciaal

look at the graph

- anonymous

ohh ok

- anonymous

now part B

- anonymous

wait but what does the sale an profit represent when it increases and decreases

- triciaal

change in y divided by change in x
f(5) - f(3) divided by (5-3)

- anonymous

but what does the sale an profit represent when it increases and decreases

- anonymous

nvm that

- anonymous

but last question

- anonymous

what is the equation for the graph?

- anonymous

@triciaal ?

- triciaal

yes you tell me

- anonymous

i don't know how to make an equation for it

- triciaal

|dw:1439405938151:dw|

- anonymous

ohh ok one second

- triciaal

|dw:1439405998517:dw|

- anonymous

f(x)=(x-3)^2+120?

- triciaal

|dw:1439406035909:dw|

- anonymous

how do i find a?

- anonymous

@triciaal how do i find a??

- anonymous

@ganeshie8 can u plz help

- anonymous

@welshfella

- anonymous

all i need is the equation and i don't know how to get to it @welshfella

- welshfella

equation for the graph can be written as f(x) = a(x - 3)^2 + 120 because the vertex is at (3,120) and a is a constant to be found

- anonymous

yes i did that too but i don't know ow to find a

- triciaal

|dw:1439406519835:dw|

- anonymous

f(x)=(x-0)(x-6)=0 is the equation?

- anonymous

?

- anonymous

hello

- welshfella

the zeroes of the equation are x=0 and x = 6
so we can plug these into
f(x) = a(x -3)^2 + 120
0 = (-3)^2 a + 120

- anonymous

i don't need the zeroes though, i only need the equation itself and thats it

- anonymous

f(x)=(x-3)^2+120 is this the equation

- welshfella

well if you find the value of a you'll get the equation

- welshfella

no - you need to find a

- anonymous

AHH whats a?!?!?

- welshfella

0 = 9 a + 120
a = ?

- anonymous

-13.33?

- welshfella

f(x) = a(x -3)^2 + 120

- welshfella

yea so we have f(x) -13.333(x - 3)^2 + 120

- anonymous

ok thank you so much!!!!

- welshfella

yw

- anonymous

@welshfella can u give @triciaal a medal for me

- welshfella

ok

- anonymous

thanks! @welshfella

- triciaal

you are welcome

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