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anonymous

  • one year ago

MEDAL AND FAN!!! A tunnel is in the shape of a parabola. The maximum height is 50 m and it is 10 m wide at the base as shown below. A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 50 meters and its width from left to right is 10 meters. What is the vertical clearance 2 m from the edge of the tunnel? I will post a picture in a second.

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  1. anonymous
    • one year ago
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    @phi

  2. anonymous
    • one year ago
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    @UsukiDoll

  3. phi
    • one year ago
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    do you know the equation of a parabola in "vertex form" ?

  4. anonymous
    • one year ago
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    is it (x-h)^2? i kind of forget

  5. anonymous
    • one year ago
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    hello?

  6. phi
    • one year ago
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    look in your notes

  7. anonymous
    • one year ago
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    ok hold on

  8. anonymous
    • one year ago
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    y = a(x-h)^2 + k

  9. anonymous
    • one year ago
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    My answer choice are: 18 m 32 m 46 m 4 m I was thinking I could approximate at 32m...

  10. phi
    • one year ago
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    where (h,k) is the vertex (in this case the "top" of the parabola) next do you have a picture ? with any luck you could sketch it. it would look like this |dw:1439209730473:dw|

  11. anonymous
    • one year ago
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    actually the turning point, or vertex is at the origin

  12. phi
    • one year ago
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    the reason to study math is to practice "thinking". (or "puzzle things out" if you like) we can draw the picture any way we like. if we use my picture, what are the coordinates of the vertex?

  13. anonymous
    • one year ago
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    (0,50)

  14. phi
    • one year ago
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    if you put those numbers into the equation what do we get ?

  15. anonymous
    • one year ago
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    y = a(x-h)^2 + k y = a(x-0)^2 + 50

  16. anonymous
    • one year ago
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    for my problem the equation would simplify to y = a(x)^2 right?

  17. phi
    • one year ago
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    ok and x-0 can be simplified to x, so y= ax^2 + 50 next, notice we are told the width (at ground level ) is 10 and with the origin at the middle, one side is at (5,0) put those numbers in for x and y and "solve for a"

  18. phi
    • one year ago
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    **y = a(x)^2 right?*** you mean y= a x^2 + 50

  19. anonymous
    • one year ago
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    i was saying for my equation...

  20. anonymous
    • one year ago
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    with the parable i am supposed to be working with. just making sure i am understanding.

  21. anonymous
    • one year ago
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    also trying to show that i am understanding what you are saying

  22. phi
    • one year ago
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    let's use my picture, then we will go back and use your picture.

  23. anonymous
    • one year ago
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    ok got it

  24. anonymous
    • one year ago
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    y = ax^2 + 50 0 = a(5)^2 + 50

  25. anonymous
    • one year ago
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    0 = 25a + 50 -50 = 25a -2 = a

  26. phi
    • one year ago
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    yes, so the equation is y= -2 x^2 + 50 next we have to interpret **vertical clearance 2 m from the edge *** all the way to the edge is 5 meters. if we move 2 m to the left, what x value is that ?

  27. anonymous
    • one year ago
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    3

  28. phi
    • one year ago
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    now we use x=3 in the equation and find y. y will be the vertical height

  29. anonymous
    • one year ago
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    y= -2 x^2 + 50 y = -2 (3)^2 + 50 y = -2 (9) + 50 y = -18 + 50 y = 32

  30. anonymous
    • one year ago
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    oh lol so if this was the parabola in the equation the answer would be 32? I think this is also the same for my parabola because we have the same dimensions. I will check

  31. phi
    • one year ago
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    looks like your guess way up top was a good one. if we draw the parabola with the vertex at (0,0), it looks like this |dw:1439210510774:dw|

  32. anonymous
    • one year ago
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    haha ok thanks

  33. anonymous
    • one year ago
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    please give me a medal @saseal

  34. phi
    • one year ago
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    yes, we will get the same answer. with the origin at the vertex, the equation is y= a x^2 now we put in the point (5,-50) and solve for a -50= a*5*5 a= -2 y= -2 x^2

  35. anonymous
    • one year ago
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    ok

  36. phi
    • one year ago
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    next, we put in x=3 to find y y= -2 *3*3 y= -2*9= -18 now we have to be careful. that is not the height. that is the distance down from the vertex the height above the "bottom" at y= -50 is the difference between -18 and -50

  37. phi
    • one year ago
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    |dw:1439210841995:dw|

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