High School Math

High School Math covers essential mathematical concepts and skills necessary for success in high school and beyond.

Algebraic FoundationsGeometry and MeasurementFunctions and Graphs
Quadratic EquationsTrigonometryStatistics and Probability
Budgeting and Personal FinanceMath in SportsMath in Technology
Effective Problem SolvingTest-Taking Tips
Algebraic Foundation...Geometry and Measure...Functions and GraphsQuadratic EquationsTrigonometryStatistics and Proba...Budgeting and Person...Math in SportsMath in TechnologyEffective Problem So...Test-Taking Tips
Advanced Topics

Quadratic Equations

What is a Quadratic Equation?

A quadratic equation has the form \( ax^2 + bx + c = 0 \), where \( a eq 0 \). These equations often lead to parabolic curves in graphs.

Solving Quadratics

There are several methods:

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

Real-World Applications

Quadratic equations are used to model:

  • The path of a thrown ball (projectiles).
  • Calculating areas and optimizing profits.
  • Physics and engineering problems.

Key Formula

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

Examples

  • Solving \( x^2 + 5x + 6 = 0 \) by factoring yields \( x = -2 \) or \( x = -3 \).

  • Using the quadratic formula for \( 2x^2 - 4x - 6 = 0 \) gives \( x = 3 \) or \( x = -1 \).

In a Nutshell

Quadratic equations involve \( x^2 \) terms and their solutions often represent real-world scenarios.

Key Terms

Discriminant
The part under the square root in the quadratic formula, \( b^2 - 4ac \), which determines the number of real solutions.
Parabola
The U-shaped curve formed by the graph of a quadratic function.
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Trigonometry