5-4 Study Guide and Intervention

Transcription

1 5 Study Guide and Intervention Graphs of Polynomial Functions Location Principle Suppose y = f() represents a polynomial function and a and b are two numbers such that f(a) < and f(b) >. Then the function has at least one real zero between a and b. Eample Determine consecutive integer values of between which each real zero of f() = is located. Then draw the graph. Make a table of values. Look at the values of f() to locate the zeros. Then use the points to sketch a graph of the function. f() 5-5 f() The changes in sign indicate that there are zeros between = and = and between = and =. 9 Eercises Graph each function by making a table of values. Determine the values of between which each real zero is located.. f() = - +. f() = f() = f() f() f(). f() = f() = f() = - + f() f() f() Lesson 5 Chapter 5 Glencoe Algebra

2 5 Maimum and Minimum Points A quadratic function has either a maimum or a minimum point on its graph. For higher degree polynomial functions, you can find turning points, which represent relative maimum or relative minimum points. Eample Graph f() = Estimate the -coordinates at which the relative maima and minima occur. Make a table of values and graph the function. f() Study Guide and Intervention indicates a relative maimum zero between =, = indicates a relative minimum 6 8 f() (continued) A relative maimum occurs at = and a relative minimum occurs at =. Eercises Graph each polynomial function. Estimate the -coordinates at which the relative maima and relative minima occur.. f() = -. f() = + -. f() = - + f(). f() = f() = f() = + - f() f() f() f() f() Chapter 5 Glencoe Algebra

3 5 Complete each of the following. a. Graph each function by making a table of values. b. Determine the consecutive values of between which each real zero is located. c. Estimate the -coordinates at which the relative maima and minima occur.. f() = - +. f() = - + f() Skills Practice f() - f() f(). f() = f() = - + f() f() f() f() - 5. f() = f() = f() f() f() f() - - Lesson 5 Chapter 5 5 Glencoe Algebra

4 5 Complete each of the following. a. Graph each function by making a table of values. b. Determine the consecutive values of between which each real zero is located. c. Estimate the -coordinates at which the relative maima and minima occur.. f() = f() = Practice f() f() f() f(). f( ) = f() = f() f() f() f() 5. PRICES The Consumer Price Inde (CPI) gives the relative price for a fied set of goods and services. The CPI from September, to July, is shown in the graph. Source: U. S. Bureau of Labor Statistics a. Describe the turning points of the graph. b. If the graph were modeled by a polynomial equation, what is the least degree the equation could have? Consumer Price Inde Months Since September, 6. LABR A town s jobless rate can be modeled by (,.), (,.9), (, 5.), (, 6.), (5,.5), (6, 5.6), (7,.5), and (8,.7). How many turning points would the graph of a polynomial function through these points have? Describe them. Chapter 5 6 Glencoe Algebra

5 5 Word Problem Practice. LANDSCAPES Jalen uses a fourthdegree polynomial to describe the shape of two hills in the background of a video game that he is helping to write. The graph of the polynomial is shown below. y. VALUE A banker models the epected value of a company in millions of dollars by the formula n - n, where n is the number of years in business. Sketch a graph of v = n - n. v n Estimate the -coordinates at which the relative maima and relative minima occur.. CNSECUTIVE NUMBERS Ms. Sanchez asks her students to write epressions to represent five consecutive integers. ne solution is -, -,, +, and +. The product of these five consecutive integers is given by the fifth degree polynomial f() = a. For what values of is f() =?. NATINAL PARKS The graph models the cross-section of Mount Rushmore. Graph Modeling Mount Rushmore y What is the smallest degree possible for the equation that corresponds with this graph? b. Sketch the graph of y = f(). y Lesson 5 Chapter 5 7 Glencoe Algebra

6 5 Enrichment Golden Rectangles Use a straightedge, a compass, and the instructions below to construct a golden rectangle.. Construct square ABCD with sides of centimeters.. Construct the midpoint of AB. Call the midpoint M.. Using M as the center, set your compass opening at MC. Construct an arc with center M that intersects AB. Call the point of intersection P.. Construct a line through P that is perpendicular to AB. 5. Etend DC so that it intersects the perpendicular. Call the intersection point Q. APQD is a golden rectangle. Check this conclusion by finding the value of QP AP. A figure consisting of similar golden rectangles is shown below. Use a compass and the instructions below to draw quarter-circle arcs that form a spiral like that found in the shell of a chambered nautilus. 6. Using A as a center, draw an arc that passes through B and C. 7. Using D as a center, draw an arc that passes through C and E. 8. Using F as a center, draw an arc that passes through E and G. 9. Continue drawing arcs, using H, K, and M as the centers. B D J C A M L K F G H E Chapter 5 8 Glencoe Algebra