7.1 An Introduction to Polynomials

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Presentation transcript:

7.1 An Introduction to Polynomials Learning Objective: To identify, classify, evaluate, add, and subtract polynomials. Also to describe the shape of the graph. Warm-up (IN)

Exponents are in decreasing order, left to right Learning Objective: To identify, classify, evaluate, add, and subtract polynomials. Also to describe the shape of the graph. Notes Monomial - A number, variable, or the product of a number and one or more variables Polynomial function - Can be written as a monomial or a sum of monomials with whole # exponents Standard form - Exponents are in decreasing order, left to right degree of a polynomial - highest exponent leading coefficient - # in front of highest exponent

Degree Type Standard form # of terms monomial constant binomial 1 Learning Objective: To identify, classify, evaluate, add, and subtract polynomials. Also to describe the shape of the graph. Degree Type Standard form # of terms monomial constant binomial 1 linear trinomial quadratic 2 Polynomial 3 cubic 4 quartic Polynomial 5 quintic Polynomial

EX 1 – classify each polynomial by degree and by number of terms Learning Objective: To identify, classify, evaluate, add, and subtract polynomials. Also to describe the shape of the graph. EX 1 – classify each polynomial by degree and by number of terms quartic cubic polynomial trinomial quadratic monomial

EX 2 – evaluate each polynomial for the given value of x. Learning Objective: To identify, classify, evaluate, add, and subtract polynomials. Also to describe the shape of the graph. EX 2 – evaluate each polynomial for the given value of x.

Learning Objective: To identify, classify, evaluate, add, and subtract polynomials. Also to describe the shape of the graph. EX 3 – add or subtract

EX 3 – graph each function. Describe its general shape Learning Objective: To identify, classify, evaluate, add, and subtract polynomials. Also to describe the shape of the graph. EX 3 – graph each function. Describe its general shape cubic S-shaped quartic w-shaped 2 turns 3 turns

Learning Objective: To identify, classify, evaluate, add, and subtract polynomials. Also to describe the shape of the graph. cubic Always increasing quartic U-shaped 0 turns 1 turn

Out – Describe how to find the degree of a polynomial function. Summary – Wow! Now, I can… HW – TBD