Algebra 1

Algebra 1 introduces students to the fundamental concepts of algebra, including variables, equations, and functions.

Advanced Topics

Quadratic Equations

What Is a Quadratic Equation?

Quadratic equations are equations where the highest exponent on the variable is 2, like \( x^2 \). They describe curved lines called parabolas.

The General Form

The standard form is \( ax^2 + bx + c = 0 \).

How Do You Solve Them?

There are several methods:

  • Factoring: Splitting into two brackets.
  • Quadratic Formula: \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)
  • Completing the Square: Rearranging into a perfect square.

Where Are Quadratics Used?

Quadratics show up in physics (launching a ball), engineering, and even in games when something moves in a curve!

Key Formula

\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

Examples

  • Solve \( x^2 - 4 = 0 \) to get \( x = 2 \) or \( x = -2 \).

  • The path of a basketball shot can be modeled by a quadratic equation.

In a Nutshell

Quadratic equations involve \( x^2 \) and create U-shaped graphs called parabolas.