## anonymous 3 years ago The curve above is the graph of a degree 3 polynomial. It goes through the point (5,−6.3). what is the polynomial please? image attached

1. anonymous

2. anonymous

a sum of several terms produces a polynomial

3. anonymous

i dont get what you mean

4. anonymous
5. anonymous

here it is ax^3+bx^2+cx+d

6. anonymous

so is 5 a and -6.3 b?

7. anonymous

nope

8. anonymous

how do i determine a an

9. anonymous

and b

10. anonymous

x=5 and y=-6.3

11. anonymous

using the graph u should find a, b, c and d

12. anonymous

how so?

13. anonymous

is it the right graph?

14. anonymous

yes

15. anonymous

x intercepts here are 2 and -2

16. cwrw238

as you can see from the graph another 2 points through which it passes are (0,-2) and (0,2)

17. anonymous

this one has a zero at $$-2$$ and a zero at $$2$$ with multiplicity 2

18. cwrw238

sorry i mean (2,0) and (-2,0)

19. anonymous

making it $a(x+2)(a-2)^2$ and your last job is to find $$a$$

20. anonymous

since you know it goes through $$(5,-6.3)$$ replace $$x$$ by $$5$$, set the result equal to $$-6.3$$ and solve for $$a$$

21. anonymous

so -6.3=(5+2)(a-2)^2?

22. anonymous

i am not sure, however, how you know it goes through that point, because it doesn't really look like it

23. anonymous

no, you need to solve for $$a$$

24. anonymous

replace $$x$$ by $$5$$ not by $$a$$

25. anonymous

$-6.3=a(5+2)(5-2)^2$

26. anonymous

$-6.3=7\times 9 a$ etc

27. anonymous

so a=-0.1

28. anonymous

??

29. cwrw238

-6.3 / 63 = - 0.1 yes

30. anonymous

so ax^3+bx^2+cx+d how do i fit all this into this format

31. cwrw238

expand -0.1(x +2)(x - 2)^2

32. anonymous

-0.1x^3 + 0.2x^2 + 0.4x - 0.8???

33. cwrw238

yes

34. anonymous

one last one

35. anonymous

The curve above is the graph of a degree 4 polynomial. It goes through the point (5,−202.5). Find the polynomial

36. anonymous

37. cwrw238

satellite confused me at first when in his 2nd post he typed a instead of x. he made a human error which we all can make sometimes.

38. anonymous

oh ok

39. cwrw238

this can be dome in similar way to the first curve there are zeros at =4 and 2 and at x=0 with duplicity 2

40. cwrw238

i meant -4

41. cwrw238

so we can write a(x+4)(x - 2)(x- 0)^2 or ax^2(x+4)(x-2)

42. cwrw238

can you continue from here?

43. cwrw238

you now need to use x = 5 y = -202.5

44. anonymous

ive got 675 for a

45. cwrw238

-202.5 = 25a * 9 * 3 = -202.5 / (25*27)

46. cwrw238

cant be 675

47. cwrw238

-0.3?

48. anonymous

oh ok

49. cwrw238

so you need to expand -0.3 x^2(x + 4\)(x - 2)

50. anonymous

thanks

51. cwrw238

yw