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Lesson 3.2 Analyzing Graphs of Polynomial Functions

Last updated over 1 year ago

15 questions

Intercept/Factored Form and Key Features of a Graph

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Examples

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On Your Own

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Lesson 3.2 Analyze Graphs of Polynomial Functions

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Question 1

1.

As we analyze a graph we can look at the following.

x-intercepts - found from our factors

Turning Points - where a graph changes from increasing to decreasing or changes from decreasing to increasing.

Absolute Extrema (Max/Min) - points that are the highest or lowest within the entire domain of the graph.

Local Extrema (Max/Min) - points that are the highest or lowest within a particular interval of a graph.

Question 2

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Question 3

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Question 4

4.

Sketch a graph of the polynomial function.

Question 5

5.

Sketch a graph of the polynomial function.

Question 6

6.

Sheena is creating an open-top box from a piece of cardboard. She forms a square flap of side length x at each corner by making a single cut (solid line) and then folding (dashed line) to form the flap. She then folds up the four sides of the box and glues each flap to the side it overlaps. What value of x, to the nearest tenth, maximizes the box’s volume?

Question 7

7.

Write a cubic or quartic function with the least degree possible in intercept form for the given graph. Assume that all x-intercepts are integers, and that the constant factor a is either 1 or -1.

Question 8

8.

What were the main mathematical concepts covered in class?

Question 9

9.

Use a graphing calculator to graph the polynomial function. Determine the x-intercepts, whether the graph crosses or is tangent to the x-axis at the x-intercept, the number of turning points, and the number and type (global, or local but not global) of any maximum or minimum values.

Question 10

10.

Use a graphing calculator to graph the polynomial function. Determine the x-intercepts, whether the graph crosses or is tangent to the x-axis at the x-intercept, the number of turning points, and the number and type (global, or local but not global) of any maximum or minimum values.

Question 11

11.

Ricardo is creating an open-top box from a piece of cardboard. He forms a square flap of side length x at each corner by making a single cut (solid line) and then folding (dashed line) to form the flap. He then folds up the four sides of the box and glues each flap to the side it overlaps. What value of x, to the nearest tenth, maximizes the box’s volume.

Question 12

12.

Sketch a graph of the polynomial function.

Question 13

13.

Sketch a graph of the polynomial function.

Question 14

14.

Write a cubic or quartic function with the least degree possible in intercept form for the given graph. Assume that all x-intercepts are integers, and that the constant factor a is either 1 or -1.

Question 15

15.

Write a cubic or quartic function with the least degree possible in intercept form for the given graph. Assume that all x-intercepts are integers, and that the constant factor a is either 1 or -1.