SAT Math

Master the essential math concepts and problem-solving skills needed to excel on the SAT.

Algebra FundamentalsWorking with FunctionsData Analysis and Statistics
Quadratic Equations and ParabolasSystems of EquationsAdvanced Geometry and Trigonometry
Budgeting and Personal FinanceSports Stats and PerformanceShopping Smarts
Pacing and Time ManagementSmart Guessing and Elimination
Algebra FundamentalsWorking with Functio...Data Analysis and St...Quadratic Equations ...Systems of EquationsAdvanced Geometry an...Budgeting and Person...Sports Stats and Per...Shopping SmartsPacing and Time Mana...Smart Guessing and E...
Advanced Topics

Quadratic Equations and Parabolas

Exploring Quadratics

Quadratic equations look like \( ax^2 + bx + c = 0 \). Their graphs are U-shaped curves called parabolas.

Solving Quadratics

  • Factoring: Split into two binomials.
  • Quadratic Formula: \( x = \frac{-b \pm \sqrt{b^2-4ac}}{2a} \)
  • Completing the Square
  • Graphing: Identify the vertex and direction (upward or downward).

Vertex and Axis of Symmetry

The vertex is the highest or lowest point: \( x = -\frac{b}{2a} \).

Why Quadratics Matter

  • Model projectile motion (throwing a ball)
  • Describe profit and revenue in business

Tips

  • Always check if the quadratic can be factored first.
  • Watch for negative signs and square roots!

Key Formula

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

Examples

  • Solving \( x^2 - 5x + 6 = 0 \) gives \( x = 2 \) and \( x = 3 \).

  • A ball thrown upward follows a parabolic path.

In a Nutshell

Quadratics model curves and help predict maximum or minimum values.

Key Terms

Parabola
The U-shaped curve of a quadratic function.
Vertex
The highest or lowest point on a parabola.
Next
Systems of Equations