Find the least squares approximation of the the data (0, 1), (1, 2), (2, 1/2) (3, 3) using the quadratic function p(x) = a_0 + a_1 x + a_2 x^2. Plot p(x) along with the data to compare.
Accepted Solution
A:
Answer:The required function is [tex]p\left(x\right)=1.325-0.675x+0.375x^2[/tex].Step-by-step explanation:The given data points are (0, 1), (1, 2), (2, 1/2) and (3, 3).Let the quadratic function is defined as[tex]p(x)=a_0+a_1x+a_2x^2[/tex] .... (1)Using graphing calculator, we get[tex]a_0=1.325[/tex][tex]a_1=-0.675[/tex][tex]a_2=0.375[/tex]Substitute [tex]a_0=1.325[/tex], [tex]a_1=-0.675[/tex] and [tex]a_2=0.375[/tex] in function (1), to find the quadratic function.[tex]p\left(x\right)=1.325-0.675x+0.375x^2[/tex]Therefore the required function is [tex]p\left(x\right)=1.325-0.675x+0.375x^2[/tex].The graph of data points and quadratic function is shown below.