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  • GKT101: General Knowledge for Teachers – Math
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  • The Quadratic Formula
    COURSE INTRODUCTION
    Course Syllabus
    Unit 1: Review of Numbers and Operational Expressions
    1.1 Whole Numbers, Integers and Absolute Value
    Practice with Whole Numbers
    Practice with Integers
    1.2: Factors and Multiples, Prime and Composite Numbers, and Divisibility Rules
    Practice with the Language of Algebra
    1.3: Fractions, Decimals, and Percentages
    Practice with Fractions and Decimals
    Practice with Percents
    1.4. Real Numbers: Rational and Irrational
    Practice with Real Numbers
    1.5: Exponents and Scientific Notation
    Practice with Integer Exponents and Scientific Notation
    1.6: Operations with Rational Numbers
    Practice with Operations
    1.7: Word Problems
    Practice with Solving Word Problems
    Unit 1 Assessment
    Unit 1 Assessment
    Unit 2: Geometry and Measurement
    2.1: Lines and Angles
    Defining Lines, Rays, and Segments
    Angles as Geometric Shapes
    Classifying Angles
    Classifying Pairs of Angles
    Practice with Lines and Angles
    2.2: Triangles
    Triangles
    Right Triangles
    Congruence of Triangles
    Practice with Triangles
    Practice with Congruent Triangles
    2.3: Quadrilaterals and Circles
    Quadrilaterals
    Review of Quadrilaterals
    Circles
    Practice with Quadrilaterals
    2.4: Three-Dimensional Shapes
    Three-Dimensional shapes
    2.5: Symmetry and Geometric Transformations
    Symmetry
    Geometric Transformations
    Translations
    2.6: Similarity and Proportional Measurements
    Defining Similarity
    Similarity of Triangles
    Solving Similar Triangles
    Application of Similar Triangles
    Practice with Similar Triangles
    2.7: Perimeter, Circumference, Area, and Volume
    Perimeter
    Area of Rectangles
    Area of Parallelograms
    Area of Triangles
    Circumference and Area of a Circle
    Surface Area
    Volume
    Volume of Three-Dimensional Shapes
    Practice with Area and Perimeter
    Practice with Surface Area
    Practice with Volume of Solids
    2.8: Units of Measurements
    Units of Length
    Units of Volume
    Units of Mass or Weight
    Converting Units of Length
    Converting Units of Time
    Converting Units of Volume
    Converting Units of Mass
    Unit Conversions
    Extra Practice with Unit Conversions
    Practice with Dimensional Analysis
    Unit 2 Assessment
    Unit 2 Assessment
    Unit 3: Algebra
    3.1: Algebraic Expressions
    Review of Variables
    Simplifying Algebraic Expressions
    Practice with Simplifying Algebraic Expressions
    Translating English to Math
    Knowledge check
    Knowledge check
    3.2: Linear Equations with One Variable
    Reviewing Equations
    Reviewing One-Step Equations
    More Review of One-Step Equations
    Two-step equations
    Equations with variables on both sides
    Equations with parenthesis
    Applications of Linear Equations
    Mixture Problems
    Practice with General Linear Equations
    Practice with Number and Geometry Problems
    3.3: Linear Inequalities with One Variable
    Review of Inequalities
    Review of One-Step Inequalities
    Two-step Inequalities and Their Applications
    General Inequalities and Their Applications
    Practice with Solving and Graphing Inequalities
    Practice with Applications of Linear Inequalities
    3.4: Quadratic Equations
    The Quadratic Formula
    More on the Quadratic Formula
    Applications of Quadratic Equations
    Practice with the Quadratic Formula
    Practice with Quadratic Applications
    3.5: Graphs of Linear Equations
    Review of the Coordinate Plane
    Linear Equations in Two Variables
    Slope
    Intercept
    Applications of Slope and Intercept
    Graphing Slope-Intercept Equations
    Writing Slope-Intercept Equations
    Point-Slope Form
    Standard Form
    Forms of linear equations: summary
    Practice with Graphs
    3.6: Graphs of Quadratic Equations
    Introduction to Parabolas
    Graphing Quadratic Equations in Vertex Form
    Graphing Quadratic Equations in Standard Form
    Practice with Graphing Quadratic Equations
    3.7: Functions
    Identifying Functions
    Evaluating Functions
    Practice with Functions
    Unit 3 Assessment
    Unit 3 Assessment
    Unit 4: Probability and Statistics
    4.1: Data Representation
    Introduction to Representing Data
    Stem-and-Leaf Plots
    Picture Graphs, Bar Graphs, and Histograms
    Frequency Tables and Dot Plots
    How to Represent Data
    Practice with Representing Data
    Misrepresenting Data
    Practice with Data Representation
    4.2: Measures of Central Tendency
    Mean, Median, and Mode
    Problems Involving Mean and Median
    Practice with Measures of the Center of Data
    More Practice with Measures of the Center of Data
    4.3: Measures of Dispersion
    Measures of Dispersion
    Practice with Measures of Dispersion
    4.4: Counting and Probability
    Introduction to Probability
    Compound Probability of Independent Events
    Independent and Dependent Events
    Practice with Dependent Events and Sample Spaces
    Practice with Conditional Probability
    4.5: Collecting Data
    Sampling and Observational Studies
    Types of Studies
    Experimental Design and Ethics
    Practice with Experimental Design and Ethics
    More Practice with Experimental Design and Ethics
    Unit 4 Assessment
    Unit 4 Assessment
    Course Feedback Survey
    Course Feedback Survey
    Certificate Final Exam
    GKT101: Certificate Final Exam
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Table of contents

  • Solving quadratics by factoring
  • Solving quadratics by factoring: leading coefficient ≠ 1
  • Solving quadratics using structure
  • Quadratics by factoring (intro) - Questions
    • Answers
  • Quadratics by factoring - Questions
    • Answers
  • Solve equations using structure - Question
    • Answers
  1. GKT101: General Knowledge for Teachers – Math
  2. Unit 3: Algebra
  3. 3.4: Quadratic Equations
  4. The Quadratic Formula

The Quadratic Formula

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Watch these videos and complete the interactive exercises.

Solving quadratics by factoring

Source: Khan Academy, https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations#x2f8bb11595b61c86:quadratic-formula-a1
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.

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Saylor Academy © 2010-2025 except as otherwise noted. Excluding course final exams, content authored by Saylor Academy is available under a Creative Commons Attribution 3.0 Unported license. Third-party materials are the copyright of their respective owners and shared under various licenses. See detailed licensing information. Saylor Academy®, Saylor.org®, and Harnessing Technology to Make Education Free® are trade names of the Constitution Foundation, a 501(c)(3) organization through which our educational activities are conducted.