Algebra 2 5.3 Discovery Name_________________________ OBJECTIVE: To understand what the graphs of polynomial functions will look like. Predict the maximum number of turns possible for the polynomial Accurately predict the left and right end behavior of the graph of any polynomial. Vocabulary 1) 2) 3) The degree of a polynomial is the highest exponent in the polynomial The leading coefficient is the coefficient of the term with the highest degree Standard form for a polynomial arranges the terms by degree, from highest to lowest Type of Function Equation of a line Equation of a quadratic Equation of a polynomial General Form of Equation Degree Leading Coefficient y = mx + b y = ax2 + bx + c y = -3x3 – 2x2 + 3x – 5 Using your graphing calculator graph each of the following equations. Complete the table and try to find any patterns regarding the behavior (shape) of the graph. Equation y = -x3 + 4x y = x4 – 5x2 + 4 y = x3 – 9x y = x4 – 4x2 + x y = -x4 + 3x2 + 2x +4 y = x5 – 3x3 + 2 Graph Degree of polynomial # of Turns (look at graph) Left end behavior (as you go to the left the picture is..) Leading Coefficient Right end behavior (as you go to the right the picture is..) rising positive rising falling negative falling rising positive rising falling negative falling rising positive rising falling negative falling rising positive rising falling negative falling rising positive rising falling negative falling rising positive rising falling negative falling If the leading coefficient is positive, and the degree is even, then the graphs at the ends will resemble__________ If the leading coefficient is positive, and the degree is odd, then the graphs at the ends will resemble___________ If the leading coefficient is negative, and the degree is even, then the graphs at the ends will resemble__________ If the leading coefficient is negative, and the degree is odd, then the graphs at the ends will resemble__________ If the degree is n, then the graph has at most ____________ turns. 1. Use the rules discovered on the front side of this sheet to answer the following questions. 2. Note that there may be more than one solution to a problem. List all the answers in alphabetical order. 3. If there is no solutions, write “NO SOLUTION” A) B) C) D) E) F) 1. Which of the graphs above are of polynomials with a positive leading coefficient? __________ 2. Which of the graphs above are of polynomials with positive leading coefficient AND an even degree? __________ 3. Which of the graphs above are of polynomials with an odd degree? __________ 4. Which of the graphs above are of polynomials with negative leading coefficient AND an odd degree? __________ 5. Which graphs have to be polynomials of at least degree 4? __________ 6. From the picture, how many roots or zeroes does equation “d” have? __________ 7. From the picture, how many y-intercepts does equation “a” have? __________ 8. For the equation y 237 x 77 14 x 3 , the degree is _________ and the left end behavior is _____________ while the right end behavior is ____________ with the maximum number of turns possible being ___________..