## anonymous one year ago Find the x-intercepts of the parabola with vertex (-4,2)and y Intercept (0,-30) Wright answer if this form (x1,y1)(x2,y2).

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1. anonymous

i would also like to know how you did it

2. Nnesha

what's the vertex form of the parabola ?

3. anonymous

(y-k)=a(x-h)^2

4. anonymous

5. Nnesha

hmm add k both sides so it would be $\huge\rm y=a(x-h)^2+k$ vertex form where (h,k) is the vertex so substitute (h,k) for ( -4,2)

6. anonymous

so like (y-2)=a(x--4)^2

7. Nnesha

ye that would work so y-intercept is (0,-30) where x =0 and y =-30 so plugin $\huge\rm -30-2=a(0-(-4))^2$ now solve for a

8. anonymous

so a =-2

9. anonymous

10. Nnesha

yes right now u can find x-intercept $\huge \rm -30-2=-2(x-(-4))^2$ solve for x let me know if you don't know how to work it out

11. anonymous

x= 0,-8 Correct?

12. Nnesha

hmm plz show a little work...

13. anonymous

im using an online calculator because the only calculator we have broke im not quite shure how to do the steps myself without it.

14. Nnesha

hmm well do you want to know how to work it out without calculator ?

15. anonymous

couldent hurt mind if i get my notepad and pencil

16. anonymous

ok i got it

17. Nnesha

alright first we can multiply negative by (-4) -1 times -4 = 4 ( negative times negative = positive ) $\huge \rm -30-2=-2(x+4))^2$ -30-2 = -32 $\huge \rm -32=-2(x+4)^2$ now we should foil (x+4)^2 (x+4)^2 is same as (x+4)(x+4)

18. Nnesha

|dw:1443017713689:dw| now we should distribute 2nd parentheses by first and 2nd term of the 2nd parentheses (foil method ) so multiply left first term by top

19. Nnesha

x(x+4) =??

20. anonymous

x^2+4x ?

21. anonymous

or dise tge 4 not have an x

22. Nnesha

yes right |dw:1443017933992:dw| and then 4(x+4) = 4x +16 now combine like terms

23. Nnesha

x^2 +4x is correct :=)

24. anonymous

ohh ok Thanks!

25. Nnesha

|dw:1443018028522:dw|alright now combine like terms

26. Nnesha

do you know what are like terms  ?

27. anonymous

no :C

28. anonymous

i beilive they are x2 and 16 4x and 4x

29. Nnesha

hmm like terms that contains same variables

30. Nnesha

x^2 is same as 1x^2 so 16 and 1x^2 are the same ?

31. Nnesha

there is a variable with 1 but no variable with 16

32. anonymous

hmm so what dose that mean?

33. Nnesha

hmm like terms that contains the same variable so 1x^2 and 16 are like terms or not ?

34. anonymous

no coreect?

35. Nnesha

yes right so just combine 4x+4x just add the coefficient here is an example 2x+4x=(2+4)x =6x

36. anonymous

well 4x+4x is 8x

37. Nnesha

yes right $-32=-2(x^2+8x+16)$ now distribute parentheses by -2

38. Nnesha

|dw:1443018609249:dw|

39. anonymous

umm ... i got 0,-8

40. anonymous

same as my answer from before so is it correct?

41. Nnesha

ohh well i was just asking abt -2(x^2+8x+16) but yes that is the answer if u use calculator not gonna force u to work by hand :D

42. anonymous

sorry iys touch im bad at numbers

43. anonymous

Sorry my its just im bad at numbers*

44. anonymous

so the asnwer to my origanal problem is 0,-8

45. anonymous

thanks

46. Nnesha

yw

47. anonymous

err 0,-8 was inccorect on my question

48. anonymous

yeet

49. Nnesha

are the solution you should write in two order pair (x1,y1)(x2,y2)

50. Nnesha

remember x-intercept when y =0 so when x=0 y=0 for 2nd order pair when x=-8 y=0