Mathematics Practices
Exploration 15-6a: Rehearsal #1 for Test
Objective: Analyze polynomial functions and their rates of change.
Answer all of these questions on separate paper. You may draw graphs on this sheet where specified. 1. Let ![]() of f. Sketch the result here.
2. By synthetic substitution , show that 2 is a
zero of
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For Problems 9–14, a freight train backs up, stops, and then goes forward. The displacement, ![]() its engine from a railroad crossing is given by
9. What is the average velocity of the train from |
Exploration 15-6b: Rehearsal #2 for Test
Objective: Analyze polynomial functions and their rates of change
1. Mr. X, the math teacher, is making up a test for his students. He wants them to find the particular equation of a cubic function, but all he will reveal about it is that for its three zeros, ![]() ![]() is true: Find the particular equation for
2. One of the zeros of
6. Let |
8. On this set of axes, sketch the graph of h.
9. At a double zero, the graph of a polynomial
function
10. What is its average velocity from
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Exploration 15-6c: Rehearsal #3 for Test, Date:
Annotated List
Objective: Analyze polynomial functions and their rates of change.
1. Find the particular equation of a polynomial function. a. From points, e.g., a cubic function containing the points (2, 7), (3, 34), (4, 91), and (5, 190). b. From zeros, e.g., a cubic function with leading coefficient 1 and zeros -5, 3, and 6. Write in factored form and then multiply and simplify . Confirm by graphing. c. From sums and products of zeros, e.g., sum= 1, product = -15, sum of pairwise products = -7. 2. Find zeros of a polynomial function. a. By graphing, e.g., ![]() Explain how you know that two of the zeros of ![]() b. By synthetic substitution, e.g., ![]() Find the complex zeros using the quadratic formula. 3. Find discontinuities in a rational function . a. Vertical asymptotes, e.g.,
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remove the removable discontinuity. Use the simplified equation to calculate the instantaneous velocity at ![]() d. Instantaneous rate by shortcut, e.g., let ![]() ![]() instantaneous rate of change of ![]() ![]() Explain how you can find the equation for ![]() from the equation for ![]() e. Instantaneous rate graphically, e.g., the figure here shows the graph of ![]() the graph at the point ![]() instantaneous rate of change of ![]() How is the line related to the graph?
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