Question 2075: can you give me a detailed way of how to solve a Parabola through 3 given points? the points are (0,2),(3,0),and (5,2). thx.
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! Assume the quadratic function (parabloa) is
y = ax^2 +bx + c,
Solve: 2 = 0+0+c =c...(1)
0 = 9a + 3b + c ...(2)
2 = 25a + 5b + c...(3)
Replace c by 2,(2),(3) become
9a + 3b + 2 =0 ...(2)
5a + b = 0...(3)
From (3): b =-5a, and goto (2), we have:
9a - 15a+ 2 =0, or -6a = -2, a = 1/3.
So, b = -5/3.
Hence, the function is y = x^2/3 - 5x/3 + 2
Also,if you notice that the parabola passing (0,2) & (5,2)(same y value)
Let y = k(x - 0)(x-5) + 2,
Set x =3, we have 0 = k*3*(-2) + 2, so k = 1/3.
Thus,we obtain the same answer y = x(x-5)/3 + 2 = x^2/3 - 5x/3 + 2
Kenny
|
|
|
