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Quadratic Equations

Topic Review on "Title":

Quadratic Equation:
A quadratic equation is a specific type of equation written on the standard form:
 where .
The Zero Product Rule:

If , then  or

Square Root Method:
If and are algebraic expressions such that then or

Completing the Square Method:
Completing the square consists of adding to both sides of an equation a positive number that can help factor a quadratic equation.

Quadratic Formula:
The solution of a quadratic equation of the form  depends on the sign of the discriminant .

Quadratic Inequality:
A quadratic inequality is a quadratic equation where the equality sign is replaced by an inequality.

Quadratic Function:
A quadratic function is a function where for each the real number  a, b, and c are real numbers with a not equal to 0.

Parabola:
A parabola is the graph of a quadratic function.

Vertex:
A vertex is the point where the parabola intersects the axis of symmetry.


Rapid Study Kit for "Title":
Flash Movie Flash Game Flash Card
Core Concept Tutorial Problem Solving Drill Review Cheat Sheet

"Title" Tutorial Summary :

This tutorial describes what a quadratic function is and its properties. The square root method is used to solve quadratic equations. Important principles such as completing the square of a quadratic equation are shown with the use of examples. The quadratic formula and the conditions under which it is used are described in this tutorial.

Quadratic Inequalities are defined and how they differ from quadratic equations. Techniques showing how you solve a quadratic inequality with roots are mentioned in this tutorial with the use of examples. Finally, quadratic equations are defined along with the use of their graphs. The vertex and the axis of symmetry are defined with the use graphical examples.


Tutorial Features:

Specific Tutorial Features:
• Step by step examples are shown to introduce quadratic equations, square root method, and graphs of quadratic functions.
• The quadratic equation and the quadratic formula are shown with the use of examples. Concept questions are asked to test the important ideals of quadratic equations.

Series Features:
• Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
• Definition slides introduce terms as they are needed.
• Visual representation of concepts
• Animated examples—worked out step by step
• A concise summary is given at the conclusion of the tutorial.


"Title" Topic List:
Quadratic Equations
Definition of a quadratic equation
Solving a quadratic equation
Square Root Method
Completing the Square Method
Quadratic Formula
Solving Quadratic Formulas
Quadratic Inequalities
Definition of quadratic inequalities
Solving quadratic inequalities with roots or no roots
Quadratic Functions
Definition of quadratic functions


See all 24 lessons in College Algebra, including concept tutorials, problem drills and cheat sheets:
Teach Yourself College Algebra Visually in 24 Hours

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