INDEX
Numbers and Sets
Complex Numbers
Exponentiation
Algebraic Transformations
Functions
Discrete Algebra
Basic Formulas
Graphics of Basic Functions
Algebraic Equations and Inequalities
Ship

Basic Conceptions and Properties

Properties of Equations and Inequalities

Graphical Interpretation of Solutions

Linear Equations and Inequalities

Linear Equations

Linear Inequalities

Linear Equations and Inequalities Involving Absolute Values

Linear Equations Involving Absolute Value

Linear Equations Involving a Few Absolute Values

Linear Inequalities Involving Absolute Value

Quadratic Equations and Inequalities

Quadratic Equations
Quadratic Equations and Quadratic Functions

Extreme Value of Quadratic Function

Quadratic Formula

Solving Quadratic Equations by Factoring

Quadratic Inequalities


Graphical Interpretation of Solutions
Key Topics Remaining:   Linear Equations » Linear Inequalities » Linear Equations Involving Absolute Values » Linear Inequalities Involving Absolute Values » Quadratic Equations » Quadratic Equations and Quadratic Functions » Extreme Value of Quadratic Function » Quadratic Formula » Solving Quadratic Equations by Factoring » Quadratic Inequalities

In order to solve graphically an equation

f ( x ) = 0,

it is necessary to find the points at which a curve

y = f ( x )

intersects or touches the x-axis.
The x-coordinates of a graph, which are common with the x-axis, are called the x-intercepts.

In order to find the x-intercepts of the function  y = f (x), set  y = 0  and solve the equation  f (x) = 0  for  x.
Solutions of an equation  f (x) = 0  are interpreted graphically as the x-intercepts of the curve  y = f (x).


Examples
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