**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 *x*-axis 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 real-number 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 third-degree 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.
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