Understanding Quadratics

Quadratic equations are a fundamental part of algebra and appear frequently in various mathematical applications. A typical quadratic equation takes the form:

ax² + bx + c = 0

Where a, b, and c are constants, and x is the variable we solve for!

Key Features of Quadratics

• Parabola Shape: Graphs of quadratic functions create a U-shaped curve called a parabola.
• Vertex: The highest or lowest point of a parabola.
• X-intercepts: Points where the parabola crosses the x-axis.

Solving Quadratic Equations

There are several methods to solve quadratic equations, including:

• Factoring
• Completing the Square
• Quadratic Formula

Quadratic Formula:

The quadratic formula is a reliable method for finding the roots of a quadratic equation:

x = (-b ± √(b²-4ac)) / (2a)

🧙‍♂️ Tip: Always remember to consider the discriminant (b²-4ac) to determine the nature of the roots!