Evaluate and graph polynomial functions. GOALS: “” Algebra 2: Notes 5.2: End Behavior of Polynomials: Zeros of Polynomials: If P is a polynomial and if.

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Presentation transcript:

Evaluate and graph polynomial functions. GOALS: “” Algebra 2: Notes 5.2: End Behavior of Polynomials: Zeros of Polynomials: If P is a polynomial and if c is a number such that P(c)=0, then we say c is a zero of P. 1.c is a zero of P 2.x=c is a root of the equation P(x)=0 3.(x-c) is a factor of P(x). Disco Fever for odd degree Leading Coefficient: Positive Negative Positive Negative YMCA for even degree

Algebra 2: Notes 5.2: Guidelines for Graphing Polynomial Functions: 1.Zeros: Factor the polynomial to find all its zeros; these are the x-intercepts of the graph. 2.Test Points: Make x-y table. Include values to determine if graph lies above or below x-axis. Include y-intercept in table. 3.End Behavior: Determine the end behavior of the polynomial. 4.Graph: Plot intercepts and other points from table. Sketch a smooth curve that passes through these points and exhibits the required end behavior.

5.2 Example 1: Polynomial function? End behavior? Check powers. All need to be positive and integers. Power of 2.5 makes it not a polynomial.Polynomial, and highest power is 4 so it is a 4 th degree polynomial or quartic. 5.2 Example 2: Graph the polynomial function. 1 st Factor if you can. 2 nd Decide if Disco or YMCA type graph. 2 nd Plug in x values and find y. 3 rd Plot points. Disco Fever graph since it is odd and left side goes up while right goes down since leading coefficient is negative.

5.2 Example 3: Synthetic division. Use synthetic division to evaluate the function when x=2. Synthetic Division: For dividing by x-c. Place c on the ledge. Put coefficients of the polynomial in row (keep the sign with the number). Bring down 1 st number. Times c by the number brought down. Place result under next number. Add the result. Then repeat till last number.