1.5 – Equations
Video 1 of 3: Quadratic Equations and Completing the Square
Video 2 of 3: Quadratic Formula
Video 3 of 3: Rational and Radical Equations
Section Notes
Properties of Equalities
![\begin{array}{|c|p{9cm}|} \hline A=B \Leftrightarrow A+c=B+c & \parbox[t]{9cm}{\textbf{Addition Principle of Equality}} Adding (or subtracting) the same value to both sides of an equation results in an equivalent equation \\ \hline A=B \Leftrightarrow cA=cB (c\not=0)& \parbox[t]{9cm}{\textbf{Multiplication Principle of Equality}} Multiplying (or dividing) a (nonzero) number to both sides of an equation results in an equivalent equation\\ \hline\end{array}](https://www.dzeymov.com/wp-content/ql-cache/quicklatex.com-fa66c2558adb022507f25047794b0767_l3.png "Rendered by QuickLaTeX.com")
Linear Equations
A Linear Equation of one variable is an equation equivalent to one of the form
where 
and 
are real numbers and 
is a variable.
Quadratic Equations
A Quadratic Equation is an equation equivalent to one of the form
where 
and 
are real numbers, and 
Zero-Product Property
Solutions of a Simple Quadratic Equation
The solutions of the equation 
are 
, and 
Completing the Square
To make the equation 
a perfect square, 
is added (typically to both sides of an equation)
The Quadratic Formula
The roots of a quadratic equation of the form , with are
The Discriminant
The Discriminant of the general quadratic equation where is
and:
1. If 
, then the equation has two distinct real solutions.
2. If 
, then the equation has exactly one real solution.
3. If 
, then the equation has no real solution.