About This Chapter
Algebra II: Graphing and Factoring Quadratic Equations Review - Chapter Summary and Learning Objectives
The chapter starts with a look at how to use tables, scatterplots and graphs in real-life situations. You'll also learn to solve quadratic equations using the FOIL method. Later lessons show you how to solve quadratic trinomials and quadratic equations through factoring. By the end of the chapter, you should hold a good grasp of the following mathematical topics:
- Scatterplots and line graphs
- Parabolas in standard, intercept and vertex form
- FOIL method for multiplying binomials
- Quadratic equations
- Quadratic trinomials
- Completing the square
|Using Tables and Graphs in the Real World||Understand how to use graphs and tables in the real world to relay information.|
|Scatterplots and Line Graphs: Definitions and Uses||Define and read the information contained in scatterplots and line graphs.|
|What Is a Parabola?||Learn about a parabola's vertex, maximum, intercepts, roots and axis of symmetry.|
|Parabolas in Standard, Intercept and Vertex Form||Identify the three forms of parabolas: the standard, intercept and vertex.|
|Multiplying Binomials Using FOIL and the Area Method||Employ the FOIL method to multiply binomials.|
|Multiplying Binomials Using FOIL and the Area Method: Practice Problems||Solve practice problems multiplying binomials using the FOIL method.|
|How to Factor Quadratic Equations: FOIL in Reverse||Use the FOIL method in reverse to factor a quadratic equation.|
|Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient||Determine how to factor a non-1 leading coefficient by grouping.|
|Solving Quadratic Trinomials by Factoring||Successfully answer quadratic equation problems with three terms.|
|How to Complete the Square||Understand how to properly complete the square.|
|Completing the Square Practice Problems||Solve practice sets that ask you to complete the square.|
|How to Solve a Quadratic Equation by Factoring||Determine how to solve a quadratic equation by factoring and using the zero product property.|
1. Using Tables and Graphs in the Real World
Tables represent data with rows and columns while graphs provide visual diagrams of data, and both are used in the real world. Explore tables, graphs, and examples of how they are used for common things, such as explaining a cell phone plan and charting population growth.
2. Scatterplots and Line Graphs: Definitions and Uses
Scatterplots and line graphs are mathematical representations used to visually analyze and interpret data. This lesson defines scatterplots and line graphs, identifies when to use each, and provides examples of their various uses.
3. What is a Parabola?
A parabola is a U shape that is created when a quadratic equation is graphed. Explore the characteristics of parabolas, how they are used in everyday life, and the defining spots of a parabola.
4. Parabolas in Standard, Intercept, and Vertex Form
The equation of a parabola can be expressed in three different forms. Explore different kinds of parabolas, and learn about the standard form, the intercept form, and the vertex form of parabola equations.
5. Multiplying Binomials Using FOIL and the Area Method
The FOIL method and the area method are two ways of multiplying binomials. Explore binomials and learn how to multiply binomials using the FOIL method, the area method, and the claw and face method.
6. Multiplying Binomials Using FOIL & the Area Method: Practice Problems
The FOIL method and area method can both help multiply binomials. See how multiplying terms using the FOIL method simplifies the equation and the area method visualizes the chart through three practice problems.
7. How to Factor Quadratic Equations: FOIL in Reverse
The FOIL method can be used in reverse to identify the standard multiples from a given equation. Discover how factoring quadratic equations using FOIL in reverse applies to multiplying binomials and breaking down equations to simplify quadratic equations.
8. Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient
Quadratic equations can be factored, even those whose leading coefficient is not '1', by using the product of binomials and isolating the pattern. Learn how to adjust the pattern and factor quadratic equations with non-1 leading coefficients using examples.
9. Solving Quadratic Trinomials by Factoring
Quadratic trinomials are polynomials with three terms that can be rewritten in a factored form consisting of two binomial factors, which will give the solutions to the quadratic equation. Learn about the standard form of a quadratic trinomial, how to set up an equation for factoring, how to determine the factors, and how to solve for the solution values.
10. How to Complete the Square
Squares can be identified and completed by turning a quadratic equation from standard form to vertex form. Learn how the transformation of the form of a quadratic equation is completed, and also how trinomials can be factored to perfect square binomials.
11. Completing the Square Practice Problems
A quadratic equation in standard form can be turned into one in vertex form by completing the square. Learn the functions of c-values, perfect square binomials, and the standard form of the quadratic equation ins and solve completing-the-square practice problems.
12. How to Solve a Quadratic Equation by Factoring
Factoring is a method of solving quadratic equations in which the equation is expressed as a product of two or more factors. Learn how to solve a quadratic equation using the factoring method through the given examples.
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Other chapters within the Algebra II: High School course
- Algebra II: Real Numbers
- Algebra II: Complex and Imaginary Numbers
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Properties of Functions Review
- Algebra II: Linear Equations Review
- Algebra II: Systems of Linear Equations Review
- Algebra II: Inequalities Review
- Algebra II: Absolute Value Review
- Algebra II: Quadratic Equations Review
- Algebra II: Factoring
- Algebra II: Polynomials
- Algebra II: Rational Expressions Review
- Algebra II: Graphing and Functions
- Algebra II: Conic Sections
- Algebra II: Roots and Radical Expressions Review
- Algebra II: Exponential and Logarithmic Functions
- Algebra II: Sequences & Series
- Algebra II: Combinatorics Review
- Algebra II: Calculations, Ratios, Percent & Proportions Review
- Algebra II: Statistics
- Algebra II: Trigonometry