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Simple Question on graphing

  1. Sep 30, 2009 #1
    1. The problem statement, all variables and given/known data
    A basketball is thrown into the air, and it's height is determined by

    h = 3/4t(20-t) where t = time.


    2. Relevant equations
    What is the greatest height the ball reaches


    3. The attempt at a solution
    Ok so i tried to graph this out but stuffed up, a bit hard to show here.

    So first i expanded the rule into
    h=15t-3/4t^2
    or
    h=-3/4t^2+15t
    Now i'm just wondering how i would graph that?
     
  2. jcsd
  3. Sep 30, 2009 #2

    rock.freak667

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    Homework Helper

    you don't need to graph it, the maximum point occurs when dh/dt=0. So find the value of t for this height hmax
     
  4. Sep 30, 2009 #3
    Ahh i see thanks a lot :D
     
  5. Oct 1, 2009 #4

    Mark44

    Staff: Mentor

    Since you posted this question in the Precalculus Math section, I assume that you haven't studied calculus just yet. The graph of the height function is a parabola that opens downward. You can find the vertex of the graph by completing the square, some exercises of which you did in another thread.

    h = -3/4t2 + 15t
    = -3/4(t2 - 20t)
    = -3/4(t2 - 20t + 100) + 75
    = -3/4(t - 10)2 + 75
     
  6. Oct 1, 2009 #5

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    By the way, I started to reply that the graph was NOT a parabola but then realized I was interpreting what Stripe wrote incorrectly. I, and, I think, most people, would interpret "3/4t(20-t)" as 3/(4t(20-t)) which certainly is NOT a parabola and has no highest point.

    Mark44 recognized that that could not correspond to a ball thrown upward and realized that Stripe meant y= (3/4)t(20-t).
     
  7. Oct 1, 2009 #6
    sorry about that it's hard trying to write equations on the computer lol
     
  8. Oct 1, 2009 #7
    = -3/4(t2 - 20t + 100) + 75
    = -3/4(t - 10)2 + 75

    So with that part where you completed the square, the + 75 is right because you do the opposide of -3/4 x 100?

    Like i thought you were supposed to do the opposite of what's in the brackets, (-100) but i'm assuming because the -3/4 you instead do the opposite of -75?
     
  9. Oct 2, 2009 #8

    Mark44

    Staff: Mentor

    In the first expression, the 100 inside the parentheses is really -75, so to keep the expression equal I had to counter that by adding 75. The net effect is that I added -75 + 75 to that expression, which makes it exactly equal to what I started with.
     
  10. Oct 2, 2009 #9

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Parentheses! (-3/4) or -(3/4) not "-3/4". And use "^" to indicate powers. (-3/4)*(t- 10)^2 is far clearer than "-3/4(t-10)2"!

    Yes, it is "+ 75" because (-3/4)(t^2- 20t+ 100)+ 75= (-3/4)t^2+ 15t- 75+ 75= (-3/4)t^2+ 15t.
     
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