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| Posted by EricB at May 9, 2008 4:44:22 AM |
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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 + 10a which 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). |