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Math 124C-4

Project B

 

Set of zeros is -3, -2, 1, 4

 

Q1.       a. List your four zeroes.

            b. Write the expression for a 4th degree polynomial with these zeroes

                 in Root Form as f(x). This is the root form of your parent function

            c. Write the expression for a 4th degree polynomial with these zeroes

                 in Function Form as f(x). This is the polynomial form of your parent

                 function

 

Q2.       a. Give the coordinates for the turning points of f(x).

            b. Identify each turning point as a local or absolute  maximum or minimum.

 

Q3.       a. Modify f(x) to compress it vertically so it fits in the Standard view

                 window on your calculator, but with the same four zeroes. This is g(x).

            b. Write g(x) in Root Form.

            c. Write g(x) in Function Form.

 

Q4.       Write the coordinates of the turning points of g(x).

 

Q5.       a. Find a new function h(x) exactly like g(x), but shifted to the right by 2.

            b. Write h(x) in Function Form.

 

Q6.       a. Modify one root of g(x) so the two rightmost zeroes are twice as far apart

                 as the two leftmost zeroes. This is k(x).

            b. Identify the regions of the domain of k(x) that are positive and negative.

 

Q7.       a. Modify k(x) so it fits in the Standard view window, but with the same

                 zeroes. This is m(x).

             b. Write m(x) in Root Form.

 

Q8.       a. Modify g(x) so that one of the zeroes (your choice) has multiplicity 2, but

                 with only four roots (that is, don't add a root, just change one root).

                 This is n(x).

            b. Give the coordinates of the turning points of n(x).

 

Q9.       a. Move k(x) vertically so it has only two zeroes. This is p(x).

            b. Write  p(x) in Function Form.

 

Q10.    Choose one of the zeroes of f(x), and any number that is not a zero of f(x).

              Using Synthetic Division, demonstrate how you can show which is a zero.