Do Now: Solve the inequality. Academy Algebra II/Trig 5.1: Polynomial Functions and Models HW: p.340 (12, 13, 17-20, 40, 41, 43, 45-47 – parts a,d,e only)

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Presentation transcript:

Do Now: Solve the inequality

Academy Algebra II/Trig 5.1: Polynomial Functions and Models HW: p.340 (12, 13, 17-20, 40, 41, 43, – parts a,d,e only) Test , 5.1, :

Vocabulary Polynomial Function = a function in the form: where, exponents are whole #’s, and coefficients are real. Standard Form = terms are written in descending order of exponents. Degree = the highest exponent.

Common Polynomial Functions DegreeTypeExample 0constantf(x)=14 1linearf(x)=5x – 7 2quadraticf(x)=x 2 +x-9 3cubicf(x)=x 3 -x 2 4quarticf(x)=x 4 +x-1

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

Identify the real zeros of a polynomial function and their multiplicity. If a polynomial is factored completely, it is easy to solve the question f(x) = 0 using the zero-product property. Example: Find the real zeros of the function:

Real Zeros For the polynomial: 7 is a zero of multiplicity 1 because the exponent on the factor of x – 7 is 1, -3 is a zero of multiplicity 2 because the exponent on the factor of x + 3 is 2. List each real zero and its multiplicity.

Form a polynomial whose real zeros and degree are given. 1.) Zeros: -3, 0, 4; degree 3 2.) Zeros: -1, multiplicity 1; 3, multiplicity 2; degree 3

Graphs of a polynomial function Graphs are smooth (no corners) and continuous (no breaks). –Determine which graphs are not polynomials.

Graphs of a polynomial function – turning points. If f is a polynomial function of degree n, then f has at most n – 1 turning points.

End Behaviors of a Polynomial Function Degree: Even Leading Coefficient: Positive Degree: Even Leading Coefficient: Negative

End Behaviors of a Polynomial Function Degree: Odd Leading Coefficient: Positive Degree: Odd Leading Coefficient: Negative

Do Now: Which of the graphs could be f(x) = x 4 + 5x 3 + 5x 2 – 5x – 3? Hint: Identify the y-intercept to help eliminate options.

Academy Algebra II/Trig 5.1: Finish HW: p (57-60 all; 65,70,74 – part f: like class work)

Graph the polynomial. Label intercepts, determine turning points, and end behavior. (May use graphing calculator for shape between intercepts.)