HELP PLEASE! WILL FAN AND GIVE MEDAL
The function f(x) = −x2 + 48x − 432 models the profit, in dollars, a game developer makes for selling a new game, where x is the number of games 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?
Part B: Determine the x-intercepts. What do these values mean in the context of the problem?

- anonymous

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- Jack1

so how do u find x intercepts?

- Jack1

x intercepts occur where y = 0

- Jack1

so put f(x) = 0 into ur equation and solve for x first

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- Jack1

its easier if u factorise the equation first tho

- anonymous

I'm not 100% sure on how to factorise it completely

- Jack1

all good:
-x^2 + 48x -432
so what 2 numbers multiply to give 432... but adds to give 48?
factors of 432 = 1,432, 2,216, 3,144, 4,108 6,72 8,54 9,48 12,36 16,27 18,24
so which 2 add to give 48
answer = 12 and 36

- Jack1

-x^2 + 48x -432
f(x) = ( -x +36 )( x - 12)

- Jack1

FOIL that:
( -x +36 )( x - 12)
( -x^2 +36x + 12x -432)

- Jack1

so, can you solve x intercepts?:
f(x) = −x2 + 48x − 432
x intercepts are when f(x) = 0
0 = −x2 + 48x − 432
0 = ( -x +36 )( x - 12)
therefore x = ??? or x = ???

- anonymous

I think I'm overthinking it xD

- anonymous

I got some crazy numbers

- triciaal

@pooja195

- Jack1

ok... well what about this: have u ever heard of the Quadratic Formula?

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- anonymous

Yes, but I haven't learned anything about it

- Jack1

u can use this on a calculator or write out shorthand and solve urself using the values from ur equation
in ur case: ur equation is:
y = ax^2 + bx + c
so a = -1
b = 48
c = -432
plug in and solve

- anonymous

12

- anonymous

Right?

- Jack1

or, easier:
0 = ( -x +36 )( x - 12)
therefore either
0 = -x +36
or
0 = x - 12
... yep, so one value is x = 12
so the other x value must be

- anonymous

36

- Jack1

perfect!
so... the hard part... what does that mean?

- Jack1

|dw:1438576993181:dw|

- anonymous

I find the vertex which is the maximum profit

- Jack1

|dw:1438577109879:dw|

- Jack1

yep, vertex = max profit... what do the x intercept indicate tho?

- anonymous

They're the number of games sold

- Jack1

yeahh... so when they hit the x axis... they're not making any money... so like if they sold 11 or few units... they'd be losing money
same as if they sold 33 or more copies... they'd be losing money

- Jack1

* sorry 37 or more copies

- anonymous

Okay I understand that

- Jack1

cools
so what's the vertex? where do u start?

- anonymous

Do I substitute the x-intercepts into the equation?

- Jack1

nah, thats over... so we want the highest point on the curve, right
have u done differentials yet? ie gradients

- anonymous

No

- Jack1

damn... i have no idea how to help u then, sorry :(

- Jack1

its the only way i know how to solve

- anonymous

Oh I think I know!

- Jack1

cool, shoot

- anonymous

There's this formula

- anonymous

Is the x-coordinate 24?

- Jack1

yep

- Jack1

so what was the formula?

- anonymous

\[x=\frac{ -b }{ 2a }\]

- Jack1

never seen it before, but hey, if it works, awesome!

- anonymous

Mhm. I think it's wrong, but is the y-coordinate 1,296?

- Jack1

no, should be 144
plug x = 24 into ur equation, u should get that

- anonymous

Yea I did something wrong there

- anonymous

But I see now

- anonymous

Thank you so much for your help!!!

- Jack1

np hey, u rock at these and good lucks

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