1. Polynomials

2. Polynomial  “many terms” The Degree of a polynomial is the largest degree of any single term – Examples:  has a degree of 5 The Leading Coefficient is the number in front of the term with the highest degree ( it will be the number in the front of the polynomial when written in descending order ). – Ex:  the leading coefficient is – 5.

3. Finding values: plug in values for x and simplify: Ex: Find each value for the given polynomial function. Use to find: 1. 2. 3. 4.

4. Graphs of Polynomial Functions: Constant Function Linear FunctionQuadratic Function (degree = 0) (degree = 1) (degree = 2) Cubic Function (deg. = 3)Quartic Functoin (deg. = 4) Quintic Function (deg. = 5)

5. The End Behavior of a polynomial graph tells what the graph does at the farthest left (as x approaches negative infinity) and farthest right (as x approaches positive infinity) on the graph. Ex: The cubic function above goes up as the graph goes to the left, so: as The cubic function goes down as the graph goes to the right, so: as Describe the end behavior of each graph: 1. 2.

6. The Zeroes of a polynomial function are the x- intercepts of the graph (the x-values that make the function = 0). – Ex: Find the zeroes of the functions above ( Y 1 = function, Y 2 = 0, 2 nd  Calc  Intersect) To find the Extrema (maximums and minimums) on the calculator: – Plug the function into Y =, then go to 2 nd  Calc  3: Min or 4: Max – Use the left bound and right bound (tell the calculator where to look), and record the ordered pair. The x- value is where the min/max occurs, and the y-value is the min/max value.

7. Point A is a Relative Maximum because it is the highest point in the immediate area (but not the highest point on the graph). Point B is a Relative Minimum because it is the lowest point in the immediate area (but not the lowest point on the entire graph). Point C is the Absolute Maximum because it is the highest point on the entire graph. There is no Absolute Minimum on this graph because the end behavior is: as and as (there is no bottom point) A B C The maximum and minimum values are the highest and lowest points on the graph.

8. Find the zeroes, extrema, and describe the end behavior for each function below: 3. 4.