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anonymous

  • one year ago

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the rainbow is the shape of a parabola. Create an equation. Use the graph below to create the equation of the rainbow parabola.

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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    y = a(x - p)(x - q) p and q are the zeros of the parabola, -6 and 6 y = a(x + 6)(x - 6) Substitute third point (0, 36) into the above equation to solve for a.

  3. anonymous
    • one year ago
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    @peachpi so i plug 0 in for x and then 36 i plug it in where the y is?

  4. anonymous
    • one year ago
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    yes

  5. anonymous
    • one year ago
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    is the answer a=-1? @peachpi

  6. anonymous
    • one year ago
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    yes

  7. anonymous
    • one year ago
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    can you help me on the next question please?? @peachpi

  8. anonymous
    • one year ago
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    if i can

  9. anonymous
    • one year ago
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    Create a table of values for a linear function. A drone is in the distance, flying upward in a straight line. It intersects the rainbow at two points. Choose the points where your drone intersects the parabola and create a table of at least four values for the function. Remember to include the two points of intersection in your table.

  10. anonymous
    • one year ago
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    3)Analyze the two functions. Answer the following reflection questions in complete sentences. What is the domain and range of the rainbow? Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not? What are the x- and y-intercepts of the rainbow? Explain what each intercept represents. Is the linear function you created positive or negative? Explain. What are the solutions or solution to the system of equations created? Explain what it or they represent.

  11. anonymous
    • one year ago
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    Pick two points that the parabola goes through and then write the equation of the line that connects them.

  12. anonymous
    • one year ago
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    What points would be the easiest?

  13. anonymous
    • one year ago
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    any two points where gridlines meet. Or if you have a graphing calculator you can pick points with integers or simple fractions

  14. anonymous
    • one year ago
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    5,5?

  15. anonymous
    • one year ago
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    i mean 5,10

  16. anonymous
    • one year ago
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    The line has to intersect the parabola twice AND move upward. You need a lower point on the left side and a higher point on the right side |dw:1433865603177:dw|

  17. anonymous
    • one year ago
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    You chose 5 on the right, but that won't really work with moving upward. Try -5 on the left, and plug it into the equation we found above to find the y-coordinate.

  18. anonymous
    • one year ago
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    i am so confused like idk where to even start.

  19. anonymous
    • one year ago
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    when you plug -5 into the equation we got for the first part, what do you get?

  20. anonymous
    • one year ago
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    what do i plug it in for? which variable

  21. anonymous
    • one year ago
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    for x. to solve for y

  22. anonymous
    • one year ago
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    so y=-1(-5+6)(-5-6)? then solve?

  23. anonymous
    • one year ago
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    yes

  24. anonymous
    • one year ago
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    y=11?

  25. anonymous
    • one year ago
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    yes. Now pick an x-value on the right side and do the same thing to get the other point. |dw:1433866189861:dw|

  26. anonymous
    • one year ago
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    -4?

  27. anonymous
    • one year ago
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    yes you can use -4

  28. anonymous
    • one year ago
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    what do i plug that in for?

  29. anonymous
    • one year ago
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    x

  30. anonymous
    • one year ago
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    y=20

  31. anonymous
    • one year ago
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    ok. great :) so now you want to find the equation of the line through (-5, 11) and (-4, 20)

  32. anonymous
    • one year ago
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    Start by finding the slope

  33. anonymous
    • one year ago
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    what is the formula again? sorry!

  34. anonymous
    • one year ago
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    |dw:1433866705637:dw|

  35. anonymous
    • one year ago
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    9/1

  36. anonymous
    • one year ago
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    yes, or just 9. So y = 9x + b. Plug in either of the 2 points to solve for b

  37. anonymous
    • one year ago
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    i can plug in 11 for y or x?

  38. anonymous
    • one year ago
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    if you plug in 11 for y, then use -5 for x

  39. anonymous
    • one year ago
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    b=56???

  40. anonymous
    • one year ago
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    yes

  41. anonymous
    • one year ago
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    so how do i answer the question in paragraph form?

  42. anonymous
    • one year ago
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    sorry, which question?

  43. anonymous
    • one year ago
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    which question did i just do all that work for question 2?

  44. anonymous
    • one year ago
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    that was for the question with the table. The equation for the line is y = 9x + 56 and you have two points on it. Find any two other random points |dw:1433867320239:dw|

  45. anonymous
    • one year ago
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    ok so that is all for #2?

  46. anonymous
    • one year ago
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    yes.

  47. anonymous
    • one year ago
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    I actually have to go. Sorry I can't help anymore

  48. anonymous
    • one year ago
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    the domain of the rainbow is [-6,6] and the range is [0,36] and it's just the shape of the rainbow. The linear function is increasing and positive and represents the path of the drone. the solutions are (-5,11 and (-4,20) and they are where the drone passes through the rainbow

  49. anonymous
    • one year ago
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    You are awesome thank you!

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