Mathematical Investigations III
Sept. 23, 2010
Name_______________________
Mods__________
Poly Quiz 2
1. Derive a sixth degree polynomial function with the following features:
bounce point at x = 5, a pass-through point at x = -4, a linear root at x = -1, and
no other real roots (NOTE: many answers are possible).
2.
Derive the polynomial function of the lowest degree for the graph below:
25
-2
-1
1
2
3
4
5
-20
-40
3. Sketch the graph of each of the following functions. Label all intercepts.
a. y1   x  1 3  x 
3
b. y1  x2  x  1
2
 x  33
4a. Compare and contrast the following two functions and their graphs using complete
sentences:





y1  x  2 x  1 x  3 and y2  x  2
2 x  1x  3
b. Given below is a sign chart for a polynomial function. Give an equation of the
function.
+
-3
+
0
+
3
4
Equation: ____________________________________
What is the lowest degree possible for this polynomial? _____________________
5. A polynomial of degree seven has at least one zero and at most 7 zeros. True or false?
Explain your answer using the terms multiplicity, factors, zeros etc.
6. Polynomial functions are nothing more than a sum of power functions: Is this
statement true? If it is then what should be true about their powers? Explain.
2
Fall 08