Name__________________________________ Have I Learned This – Alg2/Trig Unit 5 Test
Graph and Solve Polynomial Functions
Parent Signature_________________________ SOL: A2.T1, A2.T4, A2.T7, A2.T8
Teacher Signature________________________ Date of Retake___________________
Complete the statement to describe the end behavior of the graph of the function.
1. _{ }2.
Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.
3. _{ }_{4}. –3, 0, 5 5.
6. Give an example of a cubic function which has a 7. Divide.
graph that intersects the xaxis in exactly two points.
8. Two zeros of are and 8.
a. How many additional zeros are there? Explain.
b. How many turning points does the graph of f have? Explain.
c. Find all local maximums and local minimums. Then find the range of the function.
9. Using the polynomial function ,
a. Explain what effect the exponent of each factor has on the graph of the polynomial.
b. Make a sketch of the graph.
10. Evaluate the polynomial function when d = 4:
Find the realnumber solutions of the equation.
11. _{ } 12.
Factor the polynomial completely.
13. 14. _{ } 15. _{ } 16.
17. Simplify the expression. 18. Find the real zeros.
19. Sketch the graph of a thirddegree polynomial function that has one local
maximum, one local minimum, and three zeros. Identify each of these points.
20. Evaluate: 21. _{ }List the possible rational zeros of the function
22. Write the cubic function whose graph is shown. 23. Find the product:
Find all zeros of the polynomial function.
24. _{ } 25. 26.
27. Graph the polynomial function. 28. Use the graph to approximate the zeros of the function_{.}
29. Write a cubic function who’s graph passes through the points , , , and ?
30. A catering company is designing a box for packing chocolate covered nuts. The company would like the volume
of the box to be 54 cubic inches and the bottom of the box to be a square. Suppose the bottom of the box has a
width that is 3 inches smaller than the height x of the box.
