Algebra Archives - Adbhutah

Blog Complex Numbers

Complex Numbers: Detailed Explanation and 100 Examples

Introduction to Complex Numbers A complex number is a number that can be written in the form: $z = a + b i$ Where: Complex numbers extend the idea of real numbers and are used to solve equations that…

Absolute Value Functions

Absolute Value Functions: Detailed Explanation and 100 Examples

Introduction to Absolute Value Functions An absolute value function is written as $f (x) = | x |$ , where $| x |$ represents the distance of $x$ from 0 on the number line. The absolute value of $ x…

Logarithmic Functions

Logarithmic Functions: Detailed Explanation and 100 Examples

Introduction to Logarithmic Functions A logarithmic function is the inverse of an exponential function. If $a^{y} = x$ , then the logarithmic form is written as $\log_{a} (x) = y$ , which reads as “the logarithm of $ x…

Blog Graphing Functions (Linear, Quadratic, Exponential)

Graphing Functions (Linear, Quadratic, Exponential)

Graphing functions is an essential part of understanding how mathematical relationships behave visually. In this topic, we’ll explore three primary types of functions: linear, quadratic, and exponential. Each type has unique characteristics that make their graphs distinct. Linear Functions Definition…

Blog Functions and Relations

Functions and Relations: Explanation and Examples

Introduction to Functions and Relations In mathematics, relations and functions are fundamental concepts used to describe how elements from one set relate to elements of another set. A relation is simply a set of ordered pairs, where the first element…

Radical Expressions and Equations

Radical Expressions and Equations

Introduction to Radical Expressions: Radical expressions involve roots, which are inverse operations of powers. For example, the square root of a number is the number that, when multiplied by itself, gives the original number. More generally, a radical expression involves…

Rational Expressions and Equations

Rational Expressions and Equations

A rational expression is a fraction in which the numerator and the denominator are polynomials. A rational equation is an equation that contains at least one rational expression. Rational expressions can be simplified, added, subtracted, multiplied, or divided, just like…

Quadratic Equations

Quadratic Equations

A quadratic equation is an equation of the form: $a x^{2} + b x + c = 0$ Where: Quadratic equations are fundamental in algebra and appear frequently in various mathematical problems, including geometry, physics, engineering, and economics. The solutions…

Polynomials and Factoring

Polynomials and Factoring

Polynomials are algebraic expressions that consist of terms combined by addition, subtraction, and multiplication. These terms are made up of variables (like $x$ , $y$ ) raised to non-negative integer powers and constants. Factoring is the process of breaking down a polynomial…

Blog Systems of Equations

Systems of Equations

A system of equations is a collection of two or more equations with a common set of variables. The solution to a system of equations is the set of values for the variables that satisfy all of the equations simultaneously.…