Determine a mathematical model/equation for the graph below, and describe a method to validate results saying the degree of accuracy of answer.
Regarding this graph:
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My equation for the best fit curve for H is: H=-5(t-5)^2+125
(Check out the link provided below at Graphsketch.com, how my equations had evolved from a simple x^2 curve to the orange curve.)
My thinking process:
The graph resembles an inverted quadratic curve of y=x^2. Hence the maximum to the graph you have given would correspond to the minimum of the standard x^2 curve.
1. A perfect x^2 curve (see blue curve) would have the minimum at x=0.
2. To have the minimum at x=5, substitute "x-5" into "x" of the curve to get y=(x-5)^2. (see red curve)
3. However, notice that with this, the y-intercept is at 25. We want it to be 126.1 so that when we "invert" it later, the maximum will take this value. So we multiply the graph with a factor of 126.1/25 which is about 5.044 or just 5, for simplicity to get y=5(x-5)^2. (see green curve)
4. Finally, we need to invert the curve and add 125 to get y=-5(x-5)^2+125 or simply y= 125 - 5(x-5)^2 . (see orange curve)
Hope this clears the air...
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