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Algebra I

This resource covers essential concepts in algebra, focusing on adding and subtracting polynomials, identifying their degrees, and understanding standard form, leading coefficients, and special products. It also explores multiplication of polynomials and introduces quadratic functions, including their properties such as the vertex and axis of symmetry. The guide provides step-by-step instructions on graphing quadratics, using the quadratic formula, and determining solutions via the discriminant. Perfect for students looking to strengthen their algebra skills.

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Algebra I

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  1. Algebra I Chapter 8/9 Notes

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

  3. 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

  4. Section 8-1: Adding and Subtracting Polynomials, Day 1

  5. Section 8-1: Adding and Subtracting Polynomials, Day 1 Fill in the table

  6. 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)

  7. 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)

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

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

  10. Section 8-2: Multiplying polynomial by a monomial Multiply 1) 2) 3) 4)

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

  12. 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)

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

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

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

  16. 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)

  17. Section 9-1: Graphing Quadratic Functions, Day 1 Quadratic Function – Parabola – Axis of Symmetry – Vertex (min/max) -

  18. 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

  19. Section 9-1: Graphing Quadratic Functions, Day 1

  20. Section 9-1: Graphing Quadratic Functions, Day 1 Fill in the table and graph the quadratic equation

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

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

  23. Section 9-1: Graphing Quadratic Functions, Day 2

  24. 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)

  25. 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

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

  27. Section 9-1: Graphing Quadratic Functions, Day 2 Linear, Exponential, and Quadratic Functions!

  28. 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:

  29. 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.

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

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

  32. Section 9-5: The Quadratic Formula, Day 2 Discriminant –

  33. Section 9-5: The Quadratic Formula, Day 2 Discriminant – a value found by taking that determines the number of solutions

  34. 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)

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