ACT Math

A comprehensive course covering the essential math concepts and strategies needed to excel on the ACT.

Numbers and OperationsAlgebraic Expressions and EquationsGeometry Basics
Functions and GraphsProbability and StatisticsQuadratic Equations and Polynomials
Math in Personal FinanceGeometry in Real LifeStatistics in Everyday Decisions
Time Management on the ACTPlug-In and Backsolving
Numbers and Operatio...Algebraic Expression...Geometry BasicsFunctions and GraphsProbability and Stat...Quadratic Equations ...Math in Personal Fin...Geometry in Real Lif...Statistics in Everyd...Time Management on t...Plug-In and Backsolv...
Advanced Topics

Quadratic Equations and Polynomials

Parabolas and More

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

Solving Quadratics

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

Polynomials

  • An expression with several terms, like \( 3x^3 + 2x^2 - x + 5 \).

Real-World Application

Quadratics are used in physics (projectile motion), engineering, and finance (calculating profit).

ACT Focus

Recognize graphs, solve for roots, and interpret word problems involving quadratics.

Key Formula

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

Examples

  • Solving \( x^2 - 5x + 6 = 0 \) by factoring: \( (x-2)(x-3) = 0 \), so \( x = 2 \) or \( x = 3 \)

  • Using the quadratic formula on \( x^2 + 2x - 8 = 0 \) gives \( x = 2 \) or \( x = -4 \)

In a Nutshell

Quadratics pop up whenever something curves—like paths of thrown balls or profit calculations.

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Math in Personal Finance