## anonymous one year ago The cost to produce a product is modeled by the function f(x) = 5x2 − 70x + 258 where x is the number of products produced. Complete the square to determine the minimum cost of producing this product. 5(x − 7)2 + 13; The minimum cost to produce the product is $13. 5(x − 7)2 + 13; The minimum cost to produce the product is$7. 5(x − 7)2 + 258; The minimum cost to produce the product is $7. 5(x − 7)2 + 258; The minimum cost to produce the product is$258.

1. anonymous

@Nnesha

2. Nnesha

Hey, do you know how to complete the square ?

3. anonymous

Barley

4. Nnesha

oh alright $\huge\rm f(x)= 5x^2 − 70x + 258$ this is our equation where a b ,c values are $\rm Ax^2+Bx+C=0$ a=leading coefficient b=middle term c=constant term we need to complete the square of (5x^2+70x) $(5x^2+70x)+258$

5. Nnesha

first of all take out the common factor from (5x^2+70x) what is common factor(just common number not varaible ) ?

6. anonymous

2?

7. Nnesha

nope

8. Nnesha

$\huge\rm \color{Red}{5}x^2+\color{reD}{70}x$ 5 isn't divisible by 2

9. anonymous

Oh, sorry, I mixed that up with something else. So, then what 5?

10. Nnesha

yes right take out the 5 from both terms 5x^2 and 70x$5(??+??)$

11. anonymous

would you divide 70 by 5?

12. Nnesha

when you take out 5 from 5 what would you get ?

13. anonymous

0

14. Nnesha

in other words divide both terms by common factor |dw:1441211901863:dw| what do you get when yo udivide 5 x^2 by 5 and 70x/5 = ? write ur answer in the parentheses

15. anonymous

5(x^2 +14)+258?

16. Nnesha

yes right!!

17. Nnesha

wait you forgot x

18. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @gigirained 5(x^2 +14)+258? $$\color{blue}{\text{End of Quote}}$$ 5(x^2 +14x)+258 like this

19. anonymous

Oh alright

20. Nnesha

now to complete the square divide b/2 and then take square of (b/2)^2

21. Nnesha

i'll give you an example $\huge\rm x^2+Bx+C=0$ $\rm (x +\frac{ b }{ 2})^2 -(\frac{ b }{ 2})^2+C=0$ like this b = middle term

22. Nnesha

what's the middle term in that equation ?

23. anonymous

14?

24. Nnesha

yes right divide 14 by 2 then take square root of the result

25. Nnesha

$\huge\rm 5(x-\frac{ 14 }{ 2 })^2-(\frac{ 14 }{ 2 })^2 +258$

26. anonymous

5(x-7)^2 - 7^2 +258

27. Nnesha

i just noticed it supposed to be negative 14x cux in the original equation 70x is negative

28. anonymous

Okay

29. Nnesha

yes right! 7^2 = ?

30. anonymous

49

31. anonymous

do we do anything with 258?

32. Nnesha

hmm wait

33. Nnesha

ohh yeah we have common factor we have to multiply (b/2)^2 with 5

34. Nnesha

$\huge\rm \color{Red}{5}(x-7)^2-[(7)^2\times \color{ReD}{5}] +258$we should multiply (b/2)^2 wth the common factor

35. anonymous

would we multiply 7 by 5 for 49 by 5

36. Nnesha

first take square of 7 then multiply by 5

37. anonymous

245

38. Nnesha

yes right now combine like terms $5(x-7)^2\color{Red}{-245+258}$

39. anonymous

5(x-7)^2 + 13

40. Nnesha

then you will get vertex form equation of parabola $\huge\rm y=a(x-h)^2+k$ where (h,k) is the vertex if a is positive then you wll get minimum point (h,k) if a is negative you will get maximum point (h,k) (h,k) where h represents x-coordinate and k represents y -coordinate cost usually represents by y -coordinate

41. Nnesha

yes right

42. Nnesha

done!

43. anonymous

So, i dont know which one, A or B @Nnesha

44. Nnesha

reread my my comment again which coordinate represent cost ?

45. Nnesha

what's the vertex point ?

46. anonymous

7

47. anonymous

well, the answer i got was b

48. Nnesha

that's one h what is k ?

49. anonymous

13

50. anonymous

?

51. Nnesha

yes right (h,k) = (7,13) where y -coordinate represent cost

52. anonymous

how do i find the y-coordinate

53. Nnesha

(x,y) is same as (h,k) first number is x-coordinate 2nd one is y-coordinate

54. anonymous

oh lol never mind

55. anonymous

That went right over my head haha

56. Nnesha

in other words k represent cost in this question

57. anonymous

Thank you so much!

58. Nnesha

np :)