Question

Fit a second degree parabola of the form y = a + bx +cx 2 to the following data. x: 0.5 1 2 3 5 y: 3.1 6 11.2 14.8 20 ​

Answer 1

Step-by-step explanation:

Let x and y be the year and production From the normal equation na + bΣx + cΣx2  = Σy; 5a + b.0 + c. 10 = 115 5a + 10c = 115 … (1) From: aΣx + bΣx2 + cΣx3 = Σxy a.0 + b. 10 + c.0 = -25; b = -2.5 and From: aΣx2 + bΣx3 + cΣx4 = Σx2y ; a. 10 + b.0 + c.34 = 237; 10a + 34c = 237 … (2) from(1) and (2) 5a + 10c =115 × 2

10a+ 34 c=23

= 0 – 14c = -7;  ∴ c = 0.5; Put c = 0.5 in (1) 5a + 10(0.5)= 115; a = 22