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itsmichelle29

  • one year ago

Create an equation. Use the graph below to create the equation of the rainbow parabola.

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  1. itsmichelle29
    • one year ago
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  2. Michele_Laino
    • one year ago
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    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
    • one year ago
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    okay

  4. itsmichelle29
    • one year ago
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    How do i solve

  5. Michele_Laino
    • one year ago
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    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
    • one year ago
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    IDK

  7. itsmichelle29
    • one year ago
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    =(((((

  8. itsmichelle29
    • one year ago
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    no your not i check you equation onilne

  9. Michele_Laino
    • one year ago
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    if I susbstitute x=6 and y=0, into my equation I get: |dw:1436731567990:dw|

  10. Michele_Laino
    • one year ago
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    I think that I'm right, since it is a simple substitution

  11. Michele_Laino
    • one year ago
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    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
    • one year ago
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    |dw:1436731869598:dw|

  13. Michele_Laino
    • one year ago
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    hint: x=0, means x^2=x*x=0*0=0

  14. itsmichelle29
    • one year ago
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    36= ? +b

  15. itsmichelle29
    • one year ago
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    I dont understand

  16. Michele_Laino
    • one year ago
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    that's right! we have: 36=0+b or: 36=b

  17. itsmichelle29
    • one year ago
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    Okay so ?????

  18. Michele_Laino
    • one year ago
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    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
    • one year ago
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    please substitute b=36 into the first equation, wht do you get?

  20. Michele_Laino
    • one year ago
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    what*

  21. itsmichelle29
    • one year ago
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    -1

  22. Michele_Laino
    • one year ago
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    namely, you have to replace b with 36 into the first equation

  23. Michele_Laino
    • one year ago
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    perfect a=-1

  24. Michele_Laino
    • one year ago
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    now, substitute a=-1 and b=36 into this equation: \[\Large y = a{x^2} + b\] what do you get?

  25. Michele_Laino
    • one year ago
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    namely, replace a with -1 and b with 36

  26. itsmichelle29
    • one year ago
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    y=-1x^2+36

  27. Michele_Laino
    • one year ago
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    that's right! That it is your equation

  28. campbell_st
    • one year ago
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    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
    • one year ago
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    Okay thanks guys for your help

  30. Michele_Laino
    • one year ago
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    thanks! @itsmichelle29

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