## Breno 2 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. Breno

2. SerikMB

a sum of several terms produces a polynomial

3. Breno

i dont get what you mean

4. SerikMB
5. SerikMB

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

6. Breno

so is 5 a and -6.3 b?

7. SerikMB

nope

8. Breno

how do i determine a an

9. Breno

and b

10. SerikMB

x=5 and y=-6.3

11. SerikMB

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

12. Breno

how so?

13. SerikMB

is it the right graph?

14. Breno

yes

15. SerikMB

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. satellite73

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. satellite73

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

20. satellite73

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. Breno

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

22. satellite73

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

23. satellite73

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

24. satellite73

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

25. satellite73

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

26. satellite73

$-6.3=7\times 9 a$ etc

27. Breno

so a=-0.1

28. Breno

??

29. cwrw238

-6.3 / 63 = - 0.1 yes

30. Breno

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. Breno

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

33. cwrw238

yes

34. Breno

one last one

35. Breno

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

36. Breno

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. Breno

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. Breno

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. Breno

oh ok

49. cwrw238

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

50. Breno

thanks

51. cwrw238

yw