Find function which contains two pointsA certain function contains points (-3, 5) and (5, 2). We are asked to find this function,of course this will be simplest if we consider slope form equation y − y 1 = m ( x − x 1 )but could we find for general form of equation? for example quadratic? cubic?

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Find function which contains two pointsA certain function contains points (-3, 5) and (5, 2). We are asked to find this function,of course this will be simplest if we consider slope form equation  y  −      y    1    =  m  (  x  −      x    1    )but could we find for general form of equation? for example quadratic? cubic?

n8ar1val · Accepted Answer

Step 1If you want a quadratic equation   y  =  a      x    2    +  b  x  +  c, then you need at least three points to completely determine the quadratic; plugging in just two points gives you two equations in three unknowns:                    5                            =        a        (        −        3                  )          2                +        b        (        −        3        )        +        c                            2                            =        a        (        5                  )          2                +        b        (        2        )        +        c        .            This gives you the equations                    9        a        −        3        b        +        c                            =        5                            25        a        +        2        b        +        c                            =        2.            Step 2There are infinitely many solutions to these equations. Similarly, with a cubic, you need 4 points to completely determine it; with just two, you get two equations in four unknowns, after setting it up as   y  =  a      x    3    +  b      x    2    +  c  x  +  d.When you have n different points, then the method of Lagrange interpolation will produce a polynomial of degree   n  −  1 whose graph goes through the given points.

Jairo Decker · Accepted Answer

Step 1You could do this, but there would be many solutions. For a quadratic, you start with the general form  y  =  a      x    2    +  b  x  +  c  .Then substitute the x, y values given by the points.                    5                    =        9        a        −        3        b        +        c                            2                    =        25        a        +        5        b        +        c            Step 2Solve this for a,b, and c (There will be infintley many solutions. To get the solution, give c a value, then solve for a and b)

Find function which contains two points. A certain function contains points (-3,5) and (5,2). We are asked to find this function,of course this will be simplest if we consider slope form equation y−y_1=m(x-x_1) but could we find for general form of equation? for example quadratic?

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