WebGraphing.com Forum »  List all forums » »  Forum: Algebra, Pre-Algebra, and Basic Math Homework Help » » »  Thread: creating the quadratic equation for 4 (x,y) pairs that plot as a parabola » » » »  Post: Re: creating the quadratic equation for 4 (x,y) pairs that plot as a parabola Print at May 25, 2013 5:03:16 AM

 Posted by EricB at May 9, 2008 4:44:22 AM Re: creating the quadratic equation for 4 (x,y) pairs that plot as a parabola The next step is:S) 2 = 4a + 2b + c (from (2, 2))T) 4 = 9a + 3b + c (from (3,4))U) 8 = 16a + 4b + c (from (4,8) into y = ax^2 + bx + c, so you get 8 = a*4*4 + b*4 + c))and if you need it:14 = 25a + 5b + c (from (5,14) into y = ax^2 + bx + c)(you only need three equations with three unknowns, so one of these points is extra to requirements)There are lots of ways to eliminate a, b, c, for example;rearranging (S)=> c = 2 - 4a - 2b (V)put it into (T) => 4 = 9a + 3b + (2 - 4a - 2b) = 5a + b + 2 => b = 2 - 5a (W)then (complicated !) put (V) and (W) into (U) => 8 = 16a + 4(2 - 5a) + (2 - 4a - 2(2 - 5a))(b and c have now been replaced)Needs tidying up 8 = 16a + 8 - 20a + 2 - 4a - 4 + 10awhich simplifies to ...and you can figure the rest :-)A bit more working later, you end up with the right answer !(And you can check it with the fourth point, if you like).