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Homework Help: Finding the Quadratic of a Graph using Tangents

  1. Nov 4, 2006 #1
    Hey everyone,

    We've been covering tangents and derivatives etc in class recently but there is a question on the assignment that we've been given that i don't know how to do.

    The question is:
    "A quadratic equation can be fitted to any three points on a cartesian plane. The model for such an equation in y=ax + bx+ c. By substitution three seperate points (The first, middle and last data points) derive the equation of the Quadratic function that models the data."

    The situation is a cup of hot coffee is left to cool over a 50 minute period and we have been given this table of values:

    mins : Degrees Celcius
    0 :83
    5 :76.5
    8 :70.5
    11:65
    15:61
    18:57.5
    24:52.5
    35: 51
    30:47.5
    34:45
    38:43
    42:41
    45:39.5
    50:38

    From there i have plotted the time vs. temp graph and attached 3 tangents to points time (t) = 0, t = 25 & t = 50.

    at t=0 the Rate of Change or gradient was -1.85Degrees/min
    at t=25, the ROC or Gradient was -0.92degrees/min
    at t=50, the ROC or Gradient was -0.13degrees/min

    I'm not asking for you to do this for me, im just asking for the path i need to take or an idea of what i need to do...

    Thanks everyone,
    Chris :smile:
     
  2. jcsd
  3. Nov 5, 2006 #2
    Come on guys, just steer me in the right direction...Please
     
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