## anonymous one year ago What is the equation, in standard form, of a parabola that models the values in the tables x: -2,0,4 f(x): 1,5,-59

1. triciaal

|dw:1444365550534:dw|

2. triciaal

suggest substitute the values for (x,y) and solve the simultaneous equations to get a,b,c

3. anonymous

Can you explain how to do this

4. triciaal

substitute means replace now read my response again.

5. anonymous

I understand that but once i replace 1=a(-2)^2+b(-2)+c what do i do from there

6. triciaal

for each set

7. triciaal

do you know how to solve simultaneous equations? there are about 4 methods

8. anonymous

no i dont

9. triciaal

ok I will work with you what are the 3 equations?

10. triciaal

this is even simplier than i thought do you see C = 5?

11. anonymous

i guess

12. triciaal

no! if you have questions make sure you ask. it is very important for you to understand.

13. triciaal

what are the equations when you substitute the x and y values given?

14. anonymous

doesnt f(x) mean y?

15. triciaal

yes

16. triciaal

function of x

17. anonymous

so you make 3 equations and plug 1 x in for each?

18. triciaal

|dw:1444366987783:dw|

19. triciaal

y = f(x) = ax^2 + bx + c

20. triciaal

you did the first one correctly when x = -2 do the same process when x = 0 and again when x - 4

21. anonymous

ok so what do i do now that i have the 3 equations

22. triciaal

show what you have did you get C = 5?

23. anonymous

i dont understand how u got c=5

24. triciaal

did you do the substitutions?

25. anonymous

yes i got 5=a(0)^2+b(0)+c

26. triciaal

|dw:1444367515071:dw|

27. triciaal

remember zero times anything is zero

28. triciaal

show the 3rd one.

29. anonymous

-59=a(4)^2+b(4)+c

30. triciaal

and we can replace C with 5

31. triciaal

also for the first one C = 5

32. triciaal

|dw:1444367836458:dw|

33. triciaal

|dw:1444368031994:dw|

34. anonymous

what happened to -59?

35. triciaal

|dw:1444368144737:dw|

36. triciaal

|dw:1444368245388:dw|

37. triciaal

when you have an equation whatever you do to one side also do to the other to maintain the balance . always group like terms to simplify

38. triciaal

always factor when you can to use smaller numbers .

39. triciaal

by the way notice we had equations with 3 unknown we are using substitution to solve. we had the value for c and substituted in the others. we found the expressions for b and set them equal. this gave the linear equation (one unknown) and we solve for a.

40. triciaal

now that we have a,b and c we can write the general equation for f(x)

41. triciaal

please review and ask any questions if you need to clear anything up. I am short on time but you need to be able to do the problem on your own.

42. anonymous

i think i got it from here thank you

43. triciaal

yeah we are at the end you only have to write the equation.

44. triciaal

my question is do you clearly understand all what I did?

45. anonymous

Yes i do

46. triciaal

great!! review and keep practicing math is very easy with practice.