Algebraic Modeling
I need to know how to find an algebraic model for data that is quadratic?
that pretty much sums it up.. ^^
Suppose that you have values showing that when x = x1, x2, x3, x4, x5 etc, that y = y1, y2, y3, y4, y5 etc. Using the quadratic formula y = ax^2 + bx + c put in your first three known values to get
y1 = a(x1^2) + bx1 + c
y2 = a(x2^2) + bx2 + c
y3 = a(x3^2) + bx3 + c
Solve these simultaneous equations to get the values of a, b and c.
If your data is indeed a quadratic one then the x4 and y4 and all subsequent values should fit the equation as well.
I have just realised that your experimental data probably fits a quadratic function with some small errors. You would need to graph it first to check that it does look parabolic. Then sketch in the curve of best fit. Choose three points on this curve and apply the above procedure. It would obviously make things easiest to choose integer values of x, and in particular x = 0 because this gives you the value of c directly.
I have also realised that a young person looking at this might say, “Why don’t you put your values into (name) computer program which will do it for you?” I was thinking about how we would have done it many years ago before calculators let alone computers were available.
Pre Algebra: Algebraic Expressions
