1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Finding value of constants of quadric equation by experiment

  1. Jun 3, 2015 #1
    1. The problem statement, all variables and given/known data
    Suppose, the following equation describes the relation between an independent and a dependent variable physical quantities(that will be measured by experiments; for example, temperature, current, voltage etc) x & y :
    ##y = ax^2 + bx + c##
    We have to find the values of the constants (a, b, c).

    2. Relevant equations

    3. The attempt at a solution
    I have done this experiments for linear relations ,i.e. y = mx + c, where the y-intercept is c and the slope is m. I have also performed experiments for equations like ##y = ax^2## . In this case, I plotted a graph ##y## vs ##x^2##, and the slope of the straight line is ##a##.
    In this case, I can easily find the values of a, b, c by taking three pairs of (x, y) value and then solving the three equations, but it gives me less accurate answer.
    What is the best way to find the values of the constants in this experiment?
  2. jcsd
  3. Jun 3, 2015 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Since you are given x and y values, the fact that it is a quadratic is unimportant. Rather, you have a system of linear equations in three unknowns.
    Assuming you have more than three pairs of x,y values, it is overspecified. There is a standard equation for getting the least squares fit.
    If you write the system in matrix form AX=Y, (X being the vector a, b, c, and A being the matrix of 1, x, x2 values) ATA ought to be invertible. The least squares solution is X=(ATA)-1ATY.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted