## itsmichelle29 one year ago Create an equation. Use the graph below to create the equation of the rainbow parabola.

1. itsmichelle29

2. Michele_Laino

since your parabola is symmetric with respect to the y-axis, then its equation is like below: $\Large y = a{x^2} + b$ where a, and b are two coefficients to be determined

3. itsmichelle29

okay

4. itsmichelle29

How do i solve

5. Michele_Laino

now since your parabola passes at point (6,0) I substitute into the above equation x=6 and y=0, so I get: $0 = a{6^2} + b = 36a + b$ am I right?

6. itsmichelle29

IDK

7. itsmichelle29

=(((((

8. itsmichelle29

no your not i check you equation onilne

9. Michele_Laino

if I susbstitute x=6 and y=0, into my equation I get: |dw:1436731567990:dw|

10. Michele_Laino

I think that I'm right, since it is a simple substitution

11. Michele_Laino

now, since your parabola passes at point (0,36), then the coordinates of that point have to make our equation as an identity. So please substitute x=0 and y= 36 into my equation above, what do you get?

12. Michele_Laino

|dw:1436731869598:dw|

13. Michele_Laino

hint: x=0, means x^2=x*x=0*0=0

14. itsmichelle29

36= ? +b

15. itsmichelle29

I dont understand

16. Michele_Laino

that's right! we have: 36=0+b or: 36=b

17. itsmichelle29

Okay so ?????

18. Michele_Laino

so, we got this algebraic system: $\Large \left\{ \begin{gathered} 36a + b = 0 \hfill \\ \hfill \\ b = 36 \hfill \\ \end{gathered} \right.$ please solve for a and b Hint, we already know what is b, since b=36 from the second equation

19. Michele_Laino

please substitute b=36 into the first equation, wht do you get?

20. Michele_Laino

what*

21. itsmichelle29

-1

22. Michele_Laino

namely, you have to replace b with 36 into the first equation

23. Michele_Laino

perfect a=-1

24. Michele_Laino

now, substitute a=-1 and b=36 into this equation: $\Large y = a{x^2} + b$ what do you get?

25. Michele_Laino

namely, replace a with -1 and b with 36

26. itsmichelle29

y=-1x^2+36

27. Michele_Laino

that's right! That it is your equation

28. campbell_st

look at the zeros of the parabola, or where it cuts the x-axis x = -6 and x = 6 the factors that produce these zeros are x + 6 = 0 and x - 6 = 0 so the parabola is y = a(x -6)(x+6) where a is a constant this distributes to y = a(x^2 - 36) now substitute to point (0, 36) to find a so 36 = a((0)^2 - 36) or 36 = -36a solve for a hope it helps

29. itsmichelle29

Okay thanks guys for your help

30. Michele_Laino

thanks! @itsmichelle29