anonymous 5 years ago find the x intercept of a parabola with vertex (3,-2) and y intercept (0,7)

1. amistre64

(y+2) = (x-3)^2 +7 y = (x-3)^2 +5

2. amistre64

1,-6,14 3 +- sqrt(36 - 4(14))/2 ... aint see it happening

3. amistre64

yes I do lol.... its right there

4. anonymous

write it in this form (x1,y1)(x2,y2)

5. amistre64

(y+2) = (x-3)^2 +C y = (x-3)^2 +C -2 C-2 = 7; C =9 ........................................ y = (x-3)^2 +9 y = x^2 -6x +9 +9; ug, scratch that y = x^2 -6x +7 .............................. 6 +- sqrt(36 -28) sqrt(8)...2sqrt(2) ---------------- = 2 (3 + sqrt(2), 0) (3 - sqrt(2), 0) maybe lol

6. anonymous

$y=a(x-3)^2-2$ and $7=a(0-3)^2+2$ $7=9a+2$ $5=9a$ $a=\frac{5}{9}$

7. anonymous

yes?

8. anonymous

giving $y=\frac{5}{9}(x-3)^2-2$

9. anonymous

in the (x1,y1) and (x2,y2) form please, i need two intercepts

10. anonymous

ok we have the equation for the parabola. finding x- intercepts means setting y = 0 and solve for x.

11. amistre64

x^2 -6x + 7 is good

12. anonymous

in other words love $0=\frac{5}{9}(x-3)^2-2$

13. amistre64

14. amistre64

i used 0,7 ; 3,-2 ; 6,7 lol

15. anonymous

in the (x1,y1) and (x2,y2) form

16. anonymous

17. anonymous

well x-intercept means $(x_1,0)$

18. amistre64

19. anonymous

what equation did you use?

20. amistre64

x^2 -6x +7

21. anonymous

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

22. amistre64

(y-7)+9 = (x-3)^2 (y+2) = (x-3)^2

23. anonymous

boy am i dumb. i wrote $y=a(x-3)^2+2$ when it should have been $y=a(x-3)^2-2$ and $7=a(-3)^2-2$ $7=9a-2$ $9=9a$ $a=1$

24. amistre64

:) its ok lol

25. anonymous

so equation is $y=(x-3)^2-2$

26. anonymous

idk how to change it to the two points on the graph, please type it that way

27. anonymous

or if you prefer $y+2=(x-3)^2$

28. amistre64

i posted the points 2 times already...

29. amistre64

(3+sqrt(2),0) (3-sqrt(2),0) right?

30. anonymous

zeros at $3\pm \sqrt{2}$

31. anonymous

with the parenthesis? and two different points?

32. anonymous

with the parenthesis? and two different points?

33. anonymous

by inspection

34. amistre64

now that 3 and four times lol

35. anonymous

$(2 -\sqrt{3},0)$ $(2+\sqrt{3},0)$

36. amistre64

sat lol; that was backwards

37. anonymous

are the x-intercepts sorry i slowed you up

38. anonymous

oh yes it was! $(3-\sqrt{2},0)$ $(3+\sqrt{2},0)$

39. anonymous

please in the form of (x1,y1) and (x2,y2) idk what (2-sqrt of 3, 0( means...

40. anonymous

means $x_1=3-\sqrt{2}$ $y_1=0$

41. amistre64

it means the the sqrt(2) is an EXACT form of an irrational number that can only be expressed approximately in decimal form; of which we have no way of determining the requirements of since you have given us no parameters to establish them by

42. anonymous

and $x_2=3+\sqrt{2}$ $y_2=0$

43. amistre64

y = 0 exactly at: x = 3-sqrt(2) AND x= 3-sqrt(2) ; otherwise it doesnt...

44. amistre64

lol... make one of those a +sqrt(2)

45. anonymous

whats x1 and y1?

46. amistre64

x1 = 3-sqrt(2) y1 = 0

47. anonymous

its wrong

48. amistre64

x1 = 1.414213562373095048801688724209.... no, its right; you simply havent given us a means to approximate the answer.

49. amistre64

its like saying; what color is the sky? blue. wrong, its a shade of blue that is determined by whatever the criteria is for saying 'blue' in a way that is acceptable...

50. amistre64

how old am I ? the right answer depends on how accurate of an answer you want right?