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.
