Algebra 2 Notes: Graphs of Polynomial Equations Graphing essentials from Unit 4 (primarily sections 4.8 & 4.9) We will have the Unit 4 Test in approximately 3 classes

The x-intercepts of the Graph: These are the point(s) where the graph crosses the x-axis These location(s) are the zero(s)/ solution(s) that come from each factor of the polynomial equation Example:

Behavior at the x-intercepts: This is what the graph is doing at each of the x-intercepts touches & turns or passes through This is determined from the degree of the factor the intercept came from Even exponent = touch & turn Odd exponent = pass through Example: Degree = 2; touch&turn at x = 2 Degree = 1; pass through x = -3

The y-intercept of the Graph: This is the point where the graph crosses the y-axis When written in standard form, the y-intercept is always the constant term of the polynomial equation Example:

The y-intercept (continued): If the equation is not in standard form, you can solve for the y-int by replacing x with zero and solving for y/f(0) Example:

The End Behavior of the Graph: This is what the graph is doing at its ends (the very left-most “tail” and the very right-most “tail”) This is determined from the leading coefficient and degree of the first term in the polynomial equation (when written in standard form).

Summary Some or all of these pieces of information put together are enough to create or match graphs of polynomial functions Example: For g(x), determine the x-intercepts and the behavior of the graph at each. Then multiply the binomial factors to determine the leading coefficient of the polynomial, and use it to determine the end behavior of the graph. Then select a,b,c, or d according to your findings.