## anonymous one year ago 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?

1. Jack1

so how do u find x intercepts?

2. Jack1

x intercepts occur where y = 0

3. Jack1

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

4. Jack1

its easier if u factorise the equation first tho

5. anonymous

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

6. 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

7. Jack1

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

8. Jack1

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

9. 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 = ???

10. anonymous

I think I'm overthinking it xD

11. anonymous

I got some crazy numbers

12. triciaal

@pooja195

13. Jack1

14. anonymous

Yes, but I haven't learned anything about it

15. 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

16. anonymous

12

17. anonymous

Right?

18. 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

19. anonymous

36

20. Jack1

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

21. Jack1

|dw:1438576993181:dw|

22. anonymous

I find the vertex which is the maximum profit

23. Jack1

|dw:1438577109879:dw|

24. Jack1

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

25. anonymous

They're the number of games sold

26. 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

27. Jack1

* sorry 37 or more copies

28. anonymous

Okay I understand that

29. Jack1

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

30. anonymous

Do I substitute the x-intercepts into the equation?

31. Jack1

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

32. anonymous

No

33. Jack1

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

34. Jack1

its the only way i know how to solve

35. anonymous

Oh I think I know!

36. Jack1

cool, shoot

37. anonymous

There's this formula

38. anonymous

Is the x-coordinate 24?

39. Jack1

yep

40. Jack1

so what was the formula?

41. anonymous

$x=\frac{ -b }{ 2a }$

42. Jack1

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

43. anonymous

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

44. Jack1

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

45. anonymous

Yea I did something wrong there

46. anonymous

But I see now

47. anonymous

Thank you so much for your help!!!

48. Jack1

np hey, u rock at these and good lucks