anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Jack1
  • Jack1
so how do u find x intercepts?
Jack1
  • Jack1
x intercepts occur where y = 0
Jack1
  • Jack1
so put f(x) = 0 into ur equation and solve for x first

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Jack1
  • Jack1
its easier if u factorise the equation first tho
anonymous
  • anonymous
I'm not 100% sure on how to factorise it completely
Jack1
  • 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
  • Jack1
-x^2 + 48x -432 f(x) = ( -x +36 )( x - 12)
Jack1
  • Jack1
FOIL that: ( -x +36 )( x - 12) ( -x^2 +36x + 12x -432)
Jack1
  • 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
  • anonymous
I think I'm overthinking it xD
anonymous
  • anonymous
I got some crazy numbers
triciaal
  • triciaal
@pooja195
Jack1
  • Jack1
ok... well what about this: have u ever heard of the Quadratic Formula?
anonymous
  • anonymous
Yes, but I haven't learned anything about it
Jack1
  • 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
  • anonymous
12
anonymous
  • anonymous
Right?
Jack1
  • 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
  • anonymous
36
Jack1
  • Jack1
perfect! so... the hard part... what does that mean?
Jack1
  • Jack1
|dw:1438576993181:dw|
anonymous
  • anonymous
I find the vertex which is the maximum profit
Jack1
  • Jack1
|dw:1438577109879:dw|
Jack1
  • Jack1
yep, vertex = max profit... what do the x intercept indicate tho?
anonymous
  • anonymous
They're the number of games sold
Jack1
  • 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
  • Jack1
* sorry 37 or more copies
anonymous
  • anonymous
Okay I understand that
Jack1
  • Jack1
cools so what's the vertex? where do u start?
anonymous
  • anonymous
Do I substitute the x-intercepts into the equation?
Jack1
  • Jack1
nah, thats over... so we want the highest point on the curve, right have u done differentials yet? ie gradients
anonymous
  • anonymous
No
Jack1
  • Jack1
damn... i have no idea how to help u then, sorry :(
Jack1
  • Jack1
its the only way i know how to solve
anonymous
  • anonymous
Oh I think I know!
Jack1
  • Jack1
cool, shoot
anonymous
  • anonymous
There's this formula
anonymous
  • anonymous
Is the x-coordinate 24?
Jack1
  • Jack1
yep
Jack1
  • Jack1
so what was the formula?
anonymous
  • anonymous
\[x=\frac{ -b }{ 2a }\]
Jack1
  • Jack1
never seen it before, but hey, if it works, awesome!
anonymous
  • anonymous
Mhm. I think it's wrong, but is the y-coordinate 1,296?
Jack1
  • Jack1
no, should be 144 plug x = 24 into ur equation, u should get that
anonymous
  • anonymous
Yea I did something wrong there
anonymous
  • anonymous
But I see now
anonymous
  • anonymous
Thank you so much for your help!!!
Jack1
  • Jack1
np hey, u rock at these and good lucks

Looking for something else?

Not the answer you are looking for? Search for more explanations.