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
Degree
Name 1 2 3 4 5
6 or more

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

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

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 – 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

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

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

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

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

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

23. 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) )

24. 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

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

26. 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.

27. 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:

28. 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.

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

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

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

32. 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

33. 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)