Evaluate and Graph Polynomial Functions Notes 5.2 (Day 4) Evaluate and Graph Polynomial Functions

Critical points: Relative minimum – The pit of a curve in a polynomial function Relative maximum – The peak of a curve in a polynomial function

Important! The maximum number of curves a graph can make is one less than its degree. What is the maximum number of curves each polynomial function can have?

Important! The maximum number of curves a graph can make is one less than its degree. What is the smallest possible degree of the polynomial function?

Leading coefficient: The first number in the polynomial, once the polynomial is in standard form.

Polynomials of Even Degree The “tails” of the graph will be going in the same direction Will have an odd number of relative minimums and maximums If the leading coefficient is positive, the “tails” of the graph with be pointing up ↑ If the leading coefficient is negative, the “tails” of the graph with be pointing down ↓ Hint: Think of a quadratic (parabola). makes a curve in which both tails go the same direction.

Polynomials of Odd Degree The “tails” of the graph will be going in the same direction Will have an even number of relative minimums and maximums If the leading coefficient is positive, the “tail” on the left will be pointing down ↓ and the tail on the right will be pointing up ↑ If the leading coefficient is negative, the “tail” on the left will be pointing up ↑and the tail on the right will be pointing down ↓

Leading Coefficients

Which of these graphs could be the graph of a polynomial whose leading term is ?, ?, ?, ?, ?

New Concepts Infinity -∞, +∞ “Approaches” → Where the graph is going Remember: f(x) is the same as y.

Directions: Describe the end behavior of the polynomial function by completing these statements: f(x) →__?__ as x → -∞ and f(x) → __?__ as x → +∞. f(x) →__?__ as x → -∞ This means, is y increasing or decreasing as you look at the left “tail” of your graph. If the tail is pointing up, the ? is +∞, if the tail is pointing down, the ? is -∞. Hint: The leading term is the key to success in these problems!

Describe the end behavior of the polynomial function by completing these statements: f(x) →__?__ as x → -∞ and f(x) → __?__ as x → +∞. Sketch the general shape of the polynomial function.

Describe the end behavior of the polynomial function by completing these statements: f(x) →__?__ as x → -∞ and f(x) → __?__ as x → +∞. Sketch the general shape of the polynomial function.

Homework: P 342 28-36 Graphing Polynomial Functions WS