The function f(x) = −x2 + 44x − 384 models the daily profit, in dollars, a shop makes for selling donut combos, where x is the number of combos sold and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)
Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)
CAN YOU GVM THE ANSWERS PLEASE

- anonymous

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- anonymous

@jim_thompson5910

- anonymous

@jim_thompson5910 ARE STILL THERE?

- jim_thompson5910

what do you have so far?

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## More answers

- anonymous

The function f(x) = −x2 + 44x − 384 models the daily profit, in dollars, a shop makes for selling donut combos, where x is the number of combos sold and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)
Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)

- jim_thompson5910

you already posted that

- anonymous

yea can you help me its my last question?

- jim_thompson5910

|dw:1436488305187:dw|

- jim_thompson5910

|dw:1436488324499:dw|

- jim_thompson5910

|dw:1436488354162:dw|

- jim_thompson5910

oops I meant to say "a = -1"

- anonymous

Part A: -1?
Part B: 44?
Part C: -384?

- jim_thompson5910

no

- anonymous

THATS THE ANSWERS?

- jim_thompson5910

a,b,c that i listed are the coefficients
not the answers

- jim_thompson5910

have you seen \[\Large y = ax^2 + bx + c\] before?

- jim_thompson5910

btw there is no part c

- anonymous

OH YEA MY Bad, so i need to solve that problem?

- jim_thompson5910

if a = -1 and b = 44
then what is \(\LARGE \frac{-b}{2a}\) equal to?

- anonymous

a=2 and b=2 ?

- jim_thompson5910

\[\Large \frac{-b}{2a} = \frac{-44}{2*(-1)} = ??\]

- anonymous

22?

- jim_thompson5910

yes, so x = 22 is where the vertex is
plug x = 22 into the original equation to find y

- anonymous

so whats nexts? i need to find y?

- jim_thompson5910

yes

- jim_thompson5910

|dw:1436488910837:dw|

- anonymous

-342?

- jim_thompson5910

incorrect

- jim_thompson5910

you should have gotten
-1*(22)^2+44(22) - 384 = 100

- jim_thompson5910

when x = 22, y = 100

- jim_thompson5910

|dw:1436489230679:dw|

- anonymous

oh ok, so whats next?

- jim_thompson5910

`What does this calculation mean in the context of the problem? `
what does the vertex tell us?

- anonymous

(22, 100)?

- jim_thompson5910

yeah what does it mean in the real world? how does it translate into english?

- jim_thompson5910

if you're stuck, what does x represent in this problem?

- anonymous

twenty-two

- jim_thompson5910

go back up at the top
what does it say x represents?
`where x is the...`

- anonymous

x = 22 ?

- jim_thompson5910

look at the instructions. It tells you what x means

- jim_thompson5910

I don't want the number

- jim_thompson5910

`The function f(x) = −x2 + 44x − 384 models the daily profit, in dollars, a shop makes for selling donut combos, where x is _________ and f(x) is _____________.`

- anonymous

vertex?

- jim_thompson5910

do you see what I mean? by asking to look at the instructions

- jim_thompson5910

Fill in the blanks
`The function f(x) = −x2 + 44x − 384 models the daily profit, in dollars, a shop makes for selling donut combos, where x is _________ and f(x) is _____________.`

- jim_thompson5910

scroll to the very top of the page. You posted these instructions up there

- anonymous

where x is the "number of combos sold" and f(x) is the amount of profit

- jim_thompson5910

good

- jim_thompson5910

when we say
x = 22 and y = 100
that means
when 22 combos are sold, the profit is 100 dollars

- anonymous

oh

- jim_thompson5910

(22,100) is the vertex at the highest point, so the most profit we can get is $100 and that happens when 22 combos are sold

- jim_thompson5910

this is usually where managers want to aim

- anonymous

so that the answer for part A?

- jim_thompson5910

yeah all so far for A

- anonymous

OR THAT only one part?

- jim_thompson5910

we found the vertex and then gave an explanation of what it really means

- anonymous

ok thank you and for part B?

- jim_thompson5910

solve 0 = -x^2 + 44x - 384 for x
you can use technology (graphing) or the quadratic formula

- anonymous

Part A:(22,100) is the vertex at the highest point, so the most profit we can get is $100 and that happens when 22 combos are sold
Part B:?

- jim_thompson5910

part b)
solve 0 = -x^2 + 44x - 384 for x
you can use technology (graphing) or the quadratic formula

- jim_thompson5910

desmos is a good graphing calculator
https://www.desmos.com/calculator

- jim_thompson5910

type in -x^2 + 44x - 384
then look for the x intercepts

- anonymous

TYPE IN THE CALCULATOR?

- jim_thompson5910

you see where the input box is?

- anonymous

NO :/

- jim_thompson5910

##### 1 Attachment

- anonymous

OH OKAY WAIT LET ME SEE

- anonymous

1?

- jim_thompson5910

##### 1 Attachment

- anonymous

OH IN THAT CALCULATOR I DONT KNOW HOW TO PUT X^2

- jim_thompson5910

do you see the points (12,0) and (32,0) ?

- anonymous

yes

- jim_thompson5910

you just put in x^2 like you typed

- jim_thompson5910

it understands that notation

- jim_thompson5910

(12,0) and (32,0) are the x-intercepts
x-intercept (12,0)
when x = 12, the value of y is 0
so when 12 combos are sold, the profit is $0
x-intercept (32,0)
when x = 32, the value of y is 0
so when 32 combos are sold, the profit is $0

- jim_thompson5910

anything in between x = 12 and x = 32 means you'll have positive profits
otherwise you will have 0 profit or negative profit (you lose money or owe it)

- anonymous

lose?

- jim_thompson5910

negative profit = you lost money
ie you spent more than what you made

- jim_thompson5910

example
you send $10 but you only make $6
so you lost $4 (6-10 = -4)

- anonymous

oh yea

- anonymous

so?

- jim_thompson5910

we're practically done with the problem

- jim_thompson5910

`Part B: Determine the x-intercepts. What do these values mean in the context of the problem?`
the x-intercepts are 12 and 32. As ordered pairs they are (12,0) and (32,0). They represent the points where the profit is $0. This is where you break even. You don't gain any money and you don't lose any money.

- anonymous

so thats the asnwer for part B?

- jim_thompson5910

more or less

- anonymous

ANSWER*

- anonymous

LESS?

- jim_thompson5910

huh? I don't know what you mean? I'm basically saying "yes"

- anonymous

OH I THINK YOU ARE ASK ME IS MORE OR LESS

- jim_thompson5910

ignore that portion

- anonymous

SO WHAT WITH NEED TO DO NOW?

- anonymous

WE*

- jim_thompson5910

you're done, the problem is over

- anonymous

SO WAIT THE ANSWER FOR PART B ITS: MORE OR LESS?

- jim_thompson5910

no

- jim_thompson5910

I already gave it to you. Just go back and re-read it

- anonymous

the x-intercepts are 12 and 32. As ordered pairs they are (12,0) and (32,0). They represent the points where the profit is $0. This is where you break even. You don't gain any money and you don't lose any money.

- anonymous

???

- jim_thompson5910

yeah just put that into your own words. Hopefully you understand what I mean?

- anonymous

IN my own words? i dont know

- anonymous

@jim_thompson5910 ???

- jim_thompson5910

you can do it

- anonymous

no please i can please i don't speak good english

- anonymous

:(

- jim_thompson5910

Give it your best shot. Just be confident.

- anonymous

so wait i need to write the answer in my own?

- anonymous

with my own letters?

- jim_thompson5910

yes

- anonymous

thankss for you help

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