Common Core: High School - Algebra

This subject covers the foundational concepts and skills of algebra as outlined in the Common Core standards for high school students.

Advanced Topics

Quadratic Equations and Parabolas

What Is a Quadratic Equation?

Quadratic equations are equations where the highest variable exponent is 2. They look like \( ax^2 + bx + c = 0 \).

Solving Quadratics

  • Factoring: Rewrite the equation as a product with zero.

  • Quadratic Formula: Use the special formula:

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

  • Completing the Square: Another powerful method.

Graphing: The Parabola

Quadratics graph as U-shaped curves called parabolas. The vertex is the highest or lowest point.

Real-World Connections

  • Calculating the path of a basketball shot.
  • Predicting profits or losses in business over time.

Examples

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

  • Graph \( y = x^2 - 3 \) to see a parabola opening upward.

In a Nutshell

Quadratic equations lead to parabolas, and show up in motion and patterns.