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ACT Math

Quadratic Equations and Polynomials

Learn Quadratic Equations and Polynomials in ACT Math from the production AIPH study guide.

Study guide topics

Numbers and OperationsAlgebraic Expressions and EquationsGeometry BasicsFunctions and GraphsProbability and StatisticsQuadratic Equations and PolynomialsMath in Personal FinanceGeometry in Real LifeStatistics in Everyday DecisionsTime Management on the ACTPlug-In and Backsolving

Advanced Topics

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

## 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.

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 \( x = -4 \)
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