Academy Algebra II 5.2: Evaluate and Graph Polynomial Functions

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Presentation transcript:

Academy Algebra II 5.2: Evaluate and Graph Polynomial Functions HW: p.341-342 (4-10 even, 24-27 all, 28-36 even) Quiz 5.1-5.3, 10.2: Tuesday, Oct. 28th

Vocabulary Polynomial Function = a function in the form: where , the exponents are all whole numbers, and the coefficients are all real numbers, is the leading coefficient, and is the constant term. (whole numbers: 0, 1, 2, …) (real #’s: rational & irrational)

Vocabulary Standard Form of a Polynomial = terms are written in descending order of exponents. Degree = the highest exponent.

Common Polynomial Functions Degree Type Example constant f(x)=14 1 linear f(x)=5x – 7 2 quadratic f(x)=x2+x-9 3 cubic f(x)=x3-x2 4 quartic f(x)=x4+x-1

Decide whether the function is a polynomial function Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.

Decide whether the function is a polynomial function Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.

End Behaviors of a Polynomial Function Degree: Odd Leading Coefficient: Positive Example: y = x3

End Behaviors of a Polynomial Function Degree: Odd Leading Coefficient: Negative Example: y = -x3

End Behaviors of a Polynomial Function Degree: Even Leading Coefficient: Positive Example: y = x2

End Behaviors of a Polynomial Function Degree: Even Leading Coefficient: Negative Example: y = -x2

1.) degree: 4, leading coef.: -2 Describe the end behaviors of a polynomial, given the degree and the leading coefficient. 1.) degree: 4, leading coef.: -2 2.) degree: 7, leading coef.: 4

3.) degree: 6, leading coef.: 1 Describe the end behaviors of a polynomial, given the degree and the leading coefficient. 3.) degree: 6, leading coef.: 1 4.) degree: 5, leading coef.: -6

Direct vs. Synthetic Substitution. 1.) Evaluate the polynomial for the given value of x.

Direct vs. Synthetic Substitution. 2.) Evaluate the polynomial for the given value of x.

Use the graphing calculator Input in y1, press graph (adjust window if needed) View table and plot points.

Use the graphing calculator