Question

An application of Linear Algebra to things other than lines and planes. Here’s the scenario:
You are given four points on the (x,y)-plane and you need to find a curve that “fits”. In
other words, you will need to find an equation to a curve that goes through all the four
points given. You will be asked to turn in a screenshot of your graph for this example.
I recommend you use Grapher which you can have access to on any Mac computer on
campus, or Matlab which we all have a license for now. Follow the steps below.
(a) Graph the following four points: (0,2),(1,3),(2,0),(3,8)
(b) We are going to find a degree three polynomial that fits all of these data points.
Recall that a degree three polynomial can be written as
p(x) = a + bx + cx 2 + dx 3 .
Since we want the polynomial to pass through the point (3,8), for example, we require
that
p(3) = a + 3b + 9c + 27d = 8.
Do the same for the three other points.
(c) Write the four linear equations you found above as a system of four equations and
four unknowns.
(d) Write the augmented matrix corresponding to the system of equations and solve the
system. (Recall to keep up the practice of writing the variables you are solving for
on the top of the augmented matrix.)
(e) Write the polynomial p(x) that you found. Graph the polynomial and verify that it
passes through all four points. Turn in all the work above and a screenshot of your
graph from Grapher, or matlab, etc.

Answer 1