This problem is a checkpoint for graphs, equations, and roots of polynomial functions.  

1. Sketch a graph of the polynomial function $p(x)=(x−4)(x−2)^2(x+3)^2$. Label the intercepts.

2. Write a possible equation of a polynomial function, in factored form with real coefficients, that has roots of $x=−1$, $−1−3i$, and $\sqrt { 3 }$.

3. Determine all of the roots of $p(x)=2x^4−3x^3+2x^2−6x−4$.

Check your answers by referring to the selected answers.

Ideally at this point you are comfortable working with these types of problems and can complete them correctly. If you feel that you need more confidence when completing these types of problems, then review the Polynomial Functions Checkpoint materials available at cpm.org and try the practice problems provided. From this point on, you will be expected to do problems like these correctly and with confidence.