Algebra Mastery

Introduction

Algebra is the branch of mathematics that deals with symbols and the rules for manipulating those symbols. It is about finding the unknown or putting real-life variables into equations and then solving them. Mastering algebraic concepts is essential for higher-level math and various applications in science and engineering.

Linear Equations

A linear equation is an equation of the form:

$ax + b = 0$

where $a$ and $b$ are constants and $x$ is an unknown variable. The graph of a linear equation is a straight line. Here we demonstrate the graph for the equation $y = 2x + 3$.

Quadratic Equations

A quadratic equation is an equation of the form:

$ax^2 + bx + c = 0$

where $a$, $b$, and $c$ are constants and $a \neq 0$. The graph of a quadratic equation is a parabola. Let's visualize the graph for the quadratic equation $y = x^2 - 4x + 4$.

Conclusion

Understanding linear and quadratic equations is foundational for higher mathematics. The skills acquired through solving these equations and interpreting their graphs pave the way for further studies in algebra and calculus.