Algebra I Chapter 8/9 Notes

Section 8-1: Adding and Subtracting Polynomials, Day 1 Polynomial – Binomial – Trinomial – Degree of a monomial – Degree of a polynomial –

Section 8-1: Adding and Subtracting Polynomials, Day 1 Polynomial – a monomial or the sum of monomials (also called terms) Binomial – a polynomial with 2 terms Trinomial – a polynomial with 3 terms Degree of a monomial – the sum of the exponents of all its variables Degree of a polynomial – the greatest degree of any term in the polynomial

Section 8-1: Adding and Subtracting Polynomials, Day 1 Degree Name 1 2 3 4 5 6 or more

Section 8-1: Adding and Subtracting Polynomials, Day 1 Fill in the table Expression Polynomial? Degree Monomial, Binomial, or Trinomial?

Section 8-1: Adding and Subtracting Polynomials, Day 1 Standard Form – Leading Coefficient – Ex) Write each polynomial in standard form. Identify the leading coefficient. a) b)

Section 8-1: Adding and Subtracting Polynomials, Day 1 Standard Form – the terms are in order from greatest to least degree Leading Coefficient – the coefficient of the first term when written in standard form Ex) Write each polynomial in standard form. Identify the leading coefficient. a) b)

Section 8-1: Adding and Subtracting Polynomials, Day 2 Find each sum 1) 2)

Section 8-1: Adding and Subtracting Polynomials, Day 2 Subtract the following polynomials 1) 2)

Section 8-2: Multiplying polynomial by a monomial

Section 8-2: Multiplying polynomial by a monomial Solve the equation. Distribute and combine like terms first! 1)

Section 8-3: Multiplying Polynomials, The Box Method Steps for using the box method: 1) Draw a box with dimensions based on the number of terms in the polynomials 2) Fill in the box using multiplication 3) Re-write the entire answer as one polynomial (combine any like terms) Ex) (x – 2)(3x + 4)

Section 8-3: Multiplying Polynomials, The Box Method Multiply 1) (2y – 7)(3y + 5) 2)

Section 8-3: Multiplying Polynomials, The Box Method 3) 4)

Section 8-4: Special Products Square of a sum –  Find the product 1) 2)

Section 8-4: Special Products Product of a Sum and Difference: (a + b)(a – b) Multiply 1) (x + 3)(x – 3) 2) (6y – 7)(6y + 7)

Section 9-1: Graphing Quadratic Functions, Day 1 Quadratic Function – non-linear functions that can written in the form, , where a cannot be zero Parabola – the shape of the graph of a quadratic. A ‘U’ shape either opening up or down Axis of Symmetry – the vertical line that cuts a parabola in half Vertex (min/max) – the lowest or highest point on a parabola

Section 9-1: Graphing Quadratic Functions, Day 1

Section 9-1: Graphing Quadratic Functions, Day 1 Fill in the table and graph the quadratic equation X Y 1 -1 -2 -3

Section 9-1: Graphing Quadratic Functions, Day 1 Find the vertex, axis of symmetry, and y-intercept of each graph 1) 2)

Section 9-1: Graphing Quadratic Functions, Day 1 Find the vertex, the axis of symmetry, and the y-intercept of each function. a) b)

Section 9-1: Graphing Quadratic Functions, Day 2

Section 9-1: Graphing Quadratic Functions, Day 2 For each function, determine if the function has a min or a max, find what that value is, then state the domain and range. 1) 2)

Section 9-1: Graphing Quadratic Functions, Day 2 Steps for graphing quadratics (3 points MINIMUM!) 1st point) Find and plot the vertex 2nd point) Find and plot the y-intercept*** 3rd point ) Mirror the y-intercept across the axis of symmetry and plot the 3rd point ***If the y-intercept and the vertex are the same, you must choose a different 2nd point Graph

Section 9-1: Graphing Quadratic Functions, Day 2 Graph (Plot 3 points!)

Section 9-1: Graphing Quadratic Functions, Day 2 Linear, Exponential, and Quadratic Functions! Linear Functions Exponential Functions Quadratic Functions Equation Degree Graph name What does the graph look like? End behavior As x inc., y dec. Or As x inc., y inc. As x inc., y inc. then dec. OR As x inc., y dec., then inc.

Section 9-5: The Quadratic Formula, Day 1 The Quadratic Formula: The solutions of a quadratic equation Where a does not equal zero are given by the following:

Section 9-5: The Quadratic Formula, Day 1 Steps for using the quadratic formula: Set the equation = 0 Label a, b, and c Plug a, b, c into the formula Under Radical Square Root Split into 2 Simplify the 2 fractions Solve using Q.F.

Section 9-5: The Quadratic Formula, Day 1 Solve using Q.F. Round to 1) Nearest hundredth 2)

Section 9-5: The Quadratic Formula, Day 2 Solve using Q.F. 1) 2)

Section 9-5: The Quadratic Formula, Day 2 Discriminant – Discriminant Graph Number of Solutions

Section 9-5: The Quadratic Formula, Day 2 Discriminant – a value found by taking that determines the number of solutions Discriminant Positive Zero Negative Graph Number of Solutions Two One None

Section 9-5: The Quadratic Formula, Day 2 Use the discriminant to determine how many solutions the equation has. DO NOT SOLVE! 1) 2) 3)