Unit 1 Vocabulary. A function that contains 1 or more or terms. The variables may be to any non-negative power.

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1 MODULE 1 1 Polynomial A function that contains 1 or more or terms. The variables may be to any non-negative power. 1 Modeling Mathematical modeling is the process of using, and to represent real world situations. 1 Square Root This function has the form. 1 1 Quadratic Linear A - degree polynomial function of the form ax 2 + bx + c = y and a, b, and c are real numbers. The graph is called a and has a U shape. A - degree polynomial function of the form and b and m are real numbers. The equation of a linear function has either one or two variables raised only to the power. Rating: Unit 1: Polynomial Graphs S.1

2 2 Regression Equations A regression equation models the between two or more variables. It is a measure to which researchers can one variable from another. 2 Domain 2 Range The domain is the set of values of the independent variable for which a function is defined. This is usually the - values, sometimes called the values. The range is the set of values of the dependent variable for which a function is defined. This is usually the - values, sometimes called the values Factored Form of a Polynomial Degree of a Polynomial The factored form of an expression is composed of the of factors, rather than a sum or difference of terms. A polynomial is a monomial or the or of monomials. Each monomial is called a term of the polynomial. The highest degree of a polynomial s terms. The degree of a term is the of the exponents of the variables that appear in it. Rating: Unit 1: Polynomial Graphs S.2

3 2 Coefficient A or multiplied with a variable or an unknown quantity in an algebraic term. 2 Like whose and their are the same. The coefficients may be different. 3 Tabular Method An organizational tool used to polynomials 3 Distribute To out the parts of an expression. Distributing is the opposite of. 3 Factor A number or quantity that when with another produces a given number or expression 3 Difference of Squares 2 2 a b = Rating: Unit 1: Polynomial Graphs S.3

4 3 Difference of Cubes 3 3 a b = 3 Sum of Cubes a b = 4 Monomial An algebraic expression with only term. 4 Binomial An algebraic expression of the sum or difference of terms 4 Trinomial An algebraic expression of the sum or difference of terms 4 Quotient A result obtained by one quantity by another 4 Product A result obtained by one quantity by another. 4 Reverse Tabular Method An organizational tool used to polynomials. Rating: Unit 1: Polynomial Graphs S.4

5 5 Long Division Division, usually by a number of two or more digits or a polynomial, in which each step of the process is written down. 5 Leading Term The term in a polynomial which contains the power of the variable. 5 Linear Term The term in a polynomial whose (variable) power is. 5 Quadratic Term The term in a polynomial whose power is. 5 Cubic Term The term in a polynomial whose power is. 6 Standard Form of a Polynomial The polynomial is written by degree. The term with the highest degree is first and the constant, if there is one, will be last. Rating: Unit 1: Polynomial Graphs S.5

6 7 End behavior 7 x-intercept 7 y-intercept 7 zeros 7 Multiplicity The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive or negative. The x-intercept is the at which the line crosses the x-axis The y-intercept is the at which the line crosses the y-axis A zero of a function is where the function or (bounces off) the x-axis. These are sometimes called roots, solutions or x-intercepts. The multiplicity of a zero is the of times that the zero appears as a in the polynomial. 8 Quadratic Formula The Quadratic Formula is used to find the of a quadratic (2 nd degree polynomial) function. 9 Increasing 9 Decreasing A function is increasing when the y- value as the x-value increases. A function is decreasing when the y- value as the x-value increases. Rating: Unit 1: Polynomial Graphs S.6

7 10 Cross (the x-axis) When a zero has an multiplicity, then the function will cross the x-axis at that zero. 10 Touch or Bounce (off the x-axis) When a zero has an multiplicity, then the function will touch the x-axis and then bounce away from it. 11 Relative maximum The relative maximum is the point (largest f(x) value) in a section of a graph. 11 Relative minimum The relative maximum is the point (smallest f(x) value) in a section of a graph. 12 Even function 12 Odd function A function is an even function if the graph is symmetric with respect to the. Algebraically, f(x) is an even function if and only if f(-x) =. A function is an odd function if the graph is symmetric with respect to the. Algebraically, f(x) is an odd function if and only if f(-x) =. Rating: Unit 1: Polynomial Graphs S.7

8 If the degree of the 12 Even-degree function is an number, then the function is an even-degree function. 12 Odd-degree If the degree of the function is an number, then the function is an odd-degree function. Rating: Unit 1: Polynomial Graphs S.8

9 Name: Period: Date: Activity Use one of the words to complete this Frayer diagram. Your teacher may assign you a word so ask before you start. Your word should be written in the middle oval. Be prepared to share out with the class. Unit 1: Polynomial Graphs S.9

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Section 5.1 Polynomial Functions and Models

Section 5.1 Polynomial Functions and Models Term: A term is an expression that involves only multiplication and/or division with constants and/or variables. A term is separated by + or Polynomial: A polynomial is a single term or the sum of two