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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