For the following relationship: Top Opening Parabola what method should be used to linearize the data and what is the mathematical equation that would best desribe the straight line produced?
A parabola that opens upwards is described by the relation y = a*x^2 + b, where a and b are constants with a taking on a positive value, x is the independent variable and y is the dependent variable.
If a variable y is proportional to the square of a variable x, the graph when (x, y) is plotted on the x-y axes is a parabola opening upwards.
To linearize the graph, instead of plotting the values of y and x, plot the values of y and x^2. The resultant graph is a line with equation y = k*(x^2) + b.
For example, consider a case where y is proportional to 3 times the value of x. The graph of y versus x in this case is:
If the value of y is plotted versus x^2 instead, the resulting graph is a straight line: