1
Q
Quadratic equation
A
ax^2 + bx + c = 0
2
Q
quadratic formula
A
x = -b +or- √b^2 - 4ac / 2a
3
Q
“a”
A
the coefficient of the squared term (quadratic term) in the equation
4
Q
“b”
A
the coefficient of the unsquared term (linear term) in the equation
5
Q
“c”
A
the constant in the equation
Pre-Calculus
flashcards
Decks in class (300)
# Cards
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1.1.1 The Top Ten List of Mistakes1
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1.2.1 Concepts of Inequality14
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1.2.2 Inequalities and Interval Notation5
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1.3.1 Properties of Absolute Value2
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1.3.2 Evaluating Absolute Value Expressions2
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1.4.1 An Introduction to Exponents3
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1.4.2 Evaluating Exponential Expressions3
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1.4.3 Applying the Rules of Exponents10
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1.4.4 Evaluating Expressions with Negative Exponents3
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1.5.1 Converting between Decimal and Scientific Notation1
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1.5.2 Converting Rational Exponents and Radicals3
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1.6.1 Simplifying Radical Expressions2
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1.6.2 Simplifying Radical Expressions with Variables4
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1.6.3 Rationalizing Denominators4
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1.7.1 Determining Components and Degree3
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1.7.2 Adding, Subtracting, and Multiplying Polynomials4
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1.7.3 Multiplying Big Products3
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1.7.4 Using Special Products4
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1.8.1 Factoring Using the Greatest Common Factor2
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1.8.2 Factoring by Grouping1
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1.8.3 Factoring Trinomials Completely3
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1.8.4 Factoring Trinomials: The Grouping Method1
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1.9.1 Factoring Perfect Square Trinomials1
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1.9.2 Factoring the Difference of Two Squares1
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1.9.3 Factoring the Sums and Differences of Cubes2
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1.9.4 Factoring by Any Method1
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1.10.1 Rational Expressions and Domain3
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1.10.2 Working with Fractions3
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1.10.3 Writing Rational Expressions in Lowest Terms1
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1.11.1 Multiplying and Dividing Rational Expressions2
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1.11.2 Adding and Subtracting Rational Expressions2
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1.11.3 Rewriting Complex Fractions1
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1.12.1 Introducing and Writing Complex Numbers1
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1.12.2 Rewriting Powers of i1
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1.12.3 Adding and Subtracting Complex Numbers3
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1.12.4 Multiplying Complex Numbers1
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1.12.5 Dividing Complex Numbers1
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2.1.1 An Introduction to Solving Equations6
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2.1.2 Solving a Linear Equation2
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2.1.3 Solving a Linear Equation with Rationals1
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2.1.4 Solving a Linear Equation That Has Restrictions1
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2.2.1 An Introduction to Solving Word Problems1
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2.2.2 Solving for Perimeter3
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2.2.3 Solving a Linear Geometry Problem2
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2.2.4 Solving for Consecutive Numbers3
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2.2.5 Solving to Find the Average2
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2.3.1 Solving for Constant Velocity1
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2.3.2 Solving a Problem about Work1
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2.3.3 Solving a Mixture Problem2
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2.3.4 Solving an Investment Problem1
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2.3.5 Solving Business Problems1
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2.4.1 Solving Quadratics by Factoring1
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2.4.2 Solving Quadratics by Completing the Square1
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2.4.3 Completing the Square: Another Example1
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2.5.1 Proving the Quadratic Formula1
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2.5.2 Using the Quadratic Formula5
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2.5.3 Predicting the Type of Solutions Using the Discriminant1
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2.6.1 Solving for a Squared Variable1
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2.6.2 Finding Real Number Restrictions1
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2.6.3 Solving Fancy Quadratics1
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2.7.1 An Introduction to Word Problems with Quadratics1
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2.7.2 Solving a Quadratic Geometry Problem1
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2.7.3 Solving with the Pythagorean Theorem1
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2.7.4 The Pythagorean Theorem: Another Example1
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2.8.1 Solving a Motion Problem1
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2.8.2 Solving a Projectile Problem1
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2.8.3 Solving Other Problems1
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2.9.1 Determining Extraneous Roots1
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2.9.2 Solving an Equation Containing a Radical1
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2.9.3 Solving an Equation with Two Radicals1
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2.9.4 Solving an Equation with Rational Exponents1
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2.10.1 An Introduction to Variation7
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2.10.2 Direct Proportion1
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2.10.3 Inverse Proportion1
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2.11.1 An Introduction to Solving Inequalities8
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2.11.2 Solving Compound Inequalities1
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2.11.3 More on Compound Inequalities1
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2.11.4 Solving Word Problems Involving Inequalities1
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2.12.1 Solving Quadratic Inequalities1
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2.12.2 Solving Quadratic Inequalities: Another Example1
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2.13.1 Solving Rational Inequalities2
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2.13.2 Solving Rational Inequalities: Another Example1
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2.13.3 Determining the Domains of Expressions with Radicals2
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2.14.1 Matching Number Lines with Absolute Values3
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2.14.2 Solving Absolute Value Equations1
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2.14.3 Solving Equations with Two Absolute Value Expressions1
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2.14.4 Solving Absolute Value Inequalities1
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2.14.5 Solving Absolute Value Inequalities: More Examples1
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3.1.1 Using the Cartesian System6
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3.1.2 Thinking Visually9
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3.2.1 Finding the Distance between Two Points1
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3.2.2 Finding the Second Endpoint of a Segment1
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3.3.1 Collinearity and Distance1
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3.3.2 Triangles1
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3.4.1 Finding the Center-Radius Form of the Equation of a Circle1
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3.4.2 Finding the Center and Radius of a Circle1
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3.4.3 Decoding the Circle Formula1
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3.4.4 Solving Word Problems Involving Circles1
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3.5.1 Graphing Equations by Locating Points1
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3.5.2 Finding the x- and y-Intercepts of an Equation2
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3.6.1 Functions and the Vertical Line Test2
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3.6.2 Identifying Functions1
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3.6.3 Function Notation and Finding Function Values2
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3.7.1 Determining Intervals Over Which a Function Is Increasing5
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3.7.2 Evaluating Piecewise-Defined Functions for Given Values1
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3.7.3 Solving Word Problems Involving Functions1
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3.8.1 Finding the Domain and Range of a Function2
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3.8.3 Satisfying the Domain of a Function1
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3.9.1 An Introduction to Slope1
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3.9.2 Finding the Slope of a Line Given Two Points1
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3.9.3 Interpreting Slope from a Graph4
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3.9.4 Graphing a Line Using Point and Slope2
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3.10.1 Writing an Equation in Slope-Intercept Form1
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3.10.2 Writing an Equation Given Two Points1
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3.10.3 Writing an Equation in Point-Slope Form1
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3.10.4 Matching a Slope-Intercept Equation with Its Graph1
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3.10.5 Slope for Parallel and Perpendicular Lines2
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3.11.1 Constructing Linear Function Models of Data1
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3.11.2 Linear Cost and Revenue Functions1
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3.12.1 Graphing Some Important Functions1
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3.12.2 Graphing Piecewise-Defined Functionsv1
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3.12.3 Matching Equations with Their Graphs1
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3.13.1 The Greatest Integer Function1
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3.13.2 Graphing the Greatest Integer Function1
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3.14.1 Deconstructing the Graph of a Quadratic Function1
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3.14.2 Nice-Looking Parabolas1
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3.14.3 Using Discriminants to Graph Parabolas1
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3.14.4 Maximum Height in the Real World1
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3.15.1 Finding the Vertex by Completing the Square1
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3.15.2 Using the Vertex to Write the Quadratic Equation1
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3.15.3 Finding the Maximum or Minimum of a Quadratic1
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3.15.4 Graphing Parabolas1
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3.16.1 Shifting Curves along Axes1
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3.16.2 Shifting or Translating Curves along Axes1
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3.16.3 Stretching a Graph1
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3.16.4 Graphing Quadratics Using Patterns1
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3.17.1 Determining Symmetry3
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3.17.2 Reflections2
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3.17.3 Reflecting Specific Functions1
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3.18.1 Using Operations on Functions1
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3.18.2 Composite Functions1
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3.18.3 Components of Composite Functions1
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3.18.4 Finding Functions That Form a Given Composite1
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3.18.5 Finding the Difference Quotient of a Function1
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4.1.1 Using Long Division with Polynomials1
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4.1.2 Long Division: Another Example1
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4.2.1 Using Synthetic Division with Polynomials1
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4.2.2 More Synthetic Division1
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4.3.1 The Remainder Theorem1
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4.3.2 More on the Remainder Theorem1
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4.4.1 The Factor Theorem and Its Uses1
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4.4.2 Factoring a Polynomial Given a Zero1
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4.5.1 Presenting the Rational Zero Theorem1
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4.5.2 Considering Possible Solutions1
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4.6.1 Finding Polynomials Given Zeros, Degree, and One Point1
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4.6.2 Finding all Zeros and Multiplicities of a Polynomial1
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4.6.3 Finding the Real Zeros for a Polynomial1
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4.6.4 Using Descartes' Rule of Signs1
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4.6.5 Finding the Zeros of a Polynomial from Start to Finish1
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4.7.1 Matching Graphs to Polynomial Functions1
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4.7.2 Sketching the Graphs of Basic Polynomial Functions1
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4.8.1 Understanding Rational Functions2
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4.8.2 Basic Rational Functions1
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4.9.1 Vertical Asymptotes1
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4.9.2 Horizontal Asymptotes1
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4.9.3 Graphing Rational Functions1
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4.9.4 Graphing Rational Functions: More Examples1
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4.9.5 Oblique Asymptotes1
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4.9.6 Oblique Asymptotes: Another Example1
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5.1.1 Understanding Inverse Functions1
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5.1.2 The Horizontal Line Test2
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5.1.3 Are Two Functions Inverses of Each Other?1
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5.1.4 Graphing the Inverse1
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5.2.1 Finding the Inverse of a Function1
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5.2.2 Finding the Inverse of a Function with Higher Powers1
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5.3.1 An Introduction to Exponential Functions1
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5.3.2 Graphing Exponential Functions: Useful Patterns1
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5.3.3 Graphing Exponential Functions: More Examples1
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5.4.1 Using Properties of Exponents to Solve Exponential Equations1
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5.4.2 Finding Present Value and Future Value1
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5.4.3 Finding an Interest Rate to Match Given Goals1
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5.5.1 e1
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5.5.2 Applying Exponential Functions1
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5.6.1 An Introduction to Logarithmic Functions1
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5.6.2 Converting between Exponential and Logarithmic Functions1
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5.7.1 Finding the Value of a Logarithmic Function1
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5.7.2 Solving for x in Logarithmic Equations1
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5.7.3 Graphing Logarithmic Functions1
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5.7.4 Matching Logarithmic Functions with Their Graphs1
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5.8.1 Properties of Logarithms1
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5.8.2 Expanding a Logarithmic Expression Using Properties1
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5.8.3 Combining Logarithmic Expressions1
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5.9.1 Evaluating Logarithmic Functions Using a Calculator1
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5.9.2 Using the Change of Base Formula1
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5.10.1 The Richter Scale1
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5.10.2 The Distance Modulus Formula1
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5.11.1 Solving Exponential Equations1
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5.11.2 Solving Logarithmic Equations1
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5.11.3 Solving Equations with Logarithmic Exponents1
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5.12.1 Compound Interest1
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5.12.2 Predicting Change1
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5.13.1 An Introduction to Exponential Growth and Decay1
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5.13.2 Half-Life1
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5.13.3 Newton's Law of Cooling1
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5.13.4 Continuously Compounded Interest1
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6.1.1 Finding the Quadrant in Which an Angle Lies1
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6.1.2 Finding Coterminal Angles1
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6.1.3 Finding the Complement and Supplement of an Angle1
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6.1.4 Converting between Degrees and Radians1
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6.1.5 Using the Arc Length Formula1
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6.2.1 An Introduction to the Trigonometric Functions1
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6.2.2 Evaluating Trigonometric Functions for an Angle in a Right Triangle1
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6.2.3 Finding an Angle Given the Value of a Trigonometric Function1
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6.2.4 Using Trigonometric Functions to Find Unknown Sides of Right Triangles1
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6.2.5 Finding the Height of a Building1
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6.3.1 Evaluating Trigonometric Functions for an Angle in the Coordinate Plane1
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6.3.2 Evaluating Trigonometric Functions Using the Reference Angle1
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6.3.3 Finding the Value of Trigonometric Functions Given Information about the Values of Other Trigonometric Functions1
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6.3.4 Trigonometric Functions of Important Angles1
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6.4.1 An Introduction to the Graphs of Sine and Cosine Functions1
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6.4.2 Graphing Sine or Cosine Functions with Different Coefficients1
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6.4.3 Finding Maximum and Minimum Values and Zeros of Sine and Cosine1
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6.4.4 Solving Word Problems Involving Sine or Cosine Functions1
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6.5.1 Graphing Sine and Cosine Functions with Phase Shifts1
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6.5.2 Fancy Graphing: Changes in Period, Amplitude, Vertical Shift, and Phase Shift1
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6.6.1 Graphing the Tangent, Secant, Cosecant, and Cotangent Functions1
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6.6.2 Fancy Graphing: Tangent, Secant, Cosecant, and Cotangent1
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6.6.3 Identifying a Trigonometric Function from its Graph1
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6.7.1 An Introduction to Inverse Trigonometric Functions1
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6.7.2 Evaluating Inverse Trigonometric Functions1
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6.7.3 Solving an Equation Involving an Inverse Trigonometric Function1
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6.7.4 Evaluating the Composition of a Trigonometric Function and Its Inverse1
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6.7.5 Applying Trigonometric Functions: Is He Speeding?1
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7.1.1 Fundamental Trigonometric Identities1
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7.1.2 Finding All Function Values1
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7.2.1 Simplifying a Trigonometric Expression Using Trigonometric Identities1
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7.2.2 Simplifying Trigonometric Expressions Involving Fractions1
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7.2.3 Simplifying Products of Binomials Involving Trigonometric Functions1
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7.2.4 Factoring Trigonometric Expressions1
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7.2.5 Determining Whether a Trigonometric Function Is Odd, Even, or Neither1
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7.3.1 Proving an Identity1
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7.3.2 Proving an Identity: Other Examples1
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7.4.1 Solving Trigonometric Equations1
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7.4.2 Solving Trigonometric Equations by Factoring1
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7.4.3 Solving Trigonometric Equations with Coefficients in the Argument1
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7.4.4 Solving Trigonometric Equations Using the Quadratic Formula1
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7.4.5 Solving Word Problems Involving Trigonometric Equations1
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7.5.1 Identities for Sums and Differences of Angles1
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7.5.2 Using Sum and Difference Identities1
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7.5.3 Using Sum and Difference Identities to Simplify an Expression1
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7.6.1 Confirming a Double-Angle Identity1
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7.6.2 Using Double-Angle Identities1
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7.6.3 Solving Word Problems Involving Multiple-Angle Identities1
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7.7.1 Using a Cofunction Identity1
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7.7.2 Using a Power-Reducing Identity1
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7.7.3 Using Half-Angle Identities to Solve a Trigonometric Equation1
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8.1.1 The Law of Sines1
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8.1.2 Solving a Triangle Given Two Sides and One Angle1
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8.1.3 Solving a Triangle (SAS): Another Example1
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8.1.4 The Law of Sines: An Application1
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8.2.1 The Law of Cosines1
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8.2.2 The Law of Cosines (SSS)1
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8.2.3 The Law of Cosines (SAS): An Application1
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8.2.4 Heron's Formula1
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8.3.1 An Introduction to Vectors1
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8.3.2 Finding the Magnitude and Direction of a Vector1
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8.3.3 Vector Addition and Scalar Multiplication1
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8.4.1 Finding the Components of a Vector1
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8.4.2 Finding a Unit Vector1
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8.4.3 Solving Word Problems Involving Velocity or Forces1
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8.5.1 Graphing a Complex Number and Finding Its Absolute Value1
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8.5.2 Expressing a Complex Number in Trigonometric or Polar Form1
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8.5.3 Multiplying and Dividing Complex Numbers in Trigonometric or Polar Form1
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8.6.1 Using DeMoivre's Theorem to Raise a Complex Number to a Power1
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8.6.3 More Roots of Complex Numbers1
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8.6.4 Roots of Unity1
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8.7.1 An Introduction to Polar Coordinates1
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8.7.2 Converting between Polar and Rectangular Coordinates1
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8.7.3 Converting between Polar and Rectangular Equations1
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8.7.4 Graphing Simple Polar Equations1
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8.7.5 Graphing Special Polar Equations1
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9.1.1 An Introduction to Linear Systems1
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9.1.2 Solving a System by Substitution1
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9.1.3 Solving a System by Elimination1
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9.2.1 An Introduction to Linear Systems in Three Variables1
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9.2.2 Solving Linear Systems in Three Variables1
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9.2.3 Solving Inconsistent Systems1
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9.2.4 Solving Dependent Systems1
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9.2.5 Solving Systems with Two Equations1
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9.3.1 Investments1
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9.3.2 Solving with Partial Fractions1
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9.3.3 Partial Fractions: Another Example1
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9.4.1 Solving Nonlinear Systems Using Elimination1
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9.4.2 Solving Nonlinear Systems by Substitution1
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9.5.1 An Introduction to Matrices1
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9.5.2 The Arithmetic of Matrices1
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9.5.3 Multiplying Matrices by a Scalar1
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9.5.4 Multiplying Matrices1
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Matrices5
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Conic Sections3
