CLEP College Algebra

CLEP College Algebra covers fundamental algebraic concepts and skills necessary for success in college-level mathematics courses.

Algebraic Expressions and OperationsLinear Equations and InequalitiesFunctions and Their Graphs
Quadratic Equations and ApplicationsSystems of EquationsExponents, Radicals, and Rational Expressions
Algebra in Personal FinanceAlgebra in Science and TechnologyBusiness and Everyday Problem Solving
Mastering Multiple Choice QuestionsTime Management and Test-Taking Tips
Algebraic Expression...Linear Equations and...Functions and Their ...Quadratic Equations ...Systems of EquationsExponents, Radicals,...Algebra in Personal ...Algebra in Science a...Business and Everyda...Mastering Multiple C...Time Management and ...
Advanced Topics

Quadratic Equations and Applications

Understanding Quadratics

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

Methods to Solve Quadratics

  • Factoring: Expressing the equation as a product of binomials.
  • Quadratic Formula: \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)
  • Completing the Square: Rewriting the equation to reveal the square of a binomial.

Applications

Quadratics appear in physics (projectile motion), economics (profit maximization), and engineering. They help you predict where a ball lands, how high it flies, or even optimize production costs.

Key Formula

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

Examples

  • Solve \( x^2 - 5x + 6 = 0 \) by factoring to get \( x = 2 \) and \( x = 3 \).

  • Find the maximum height of a ball thrown upward using a quadratic equation.

In a Nutshell

Quadratic equations model parabolic situations and can be solved using several algebraic techniques.

Key Terms

Parabola
The U-shaped graph of a quadratic function.
Discriminant
The part under the square root in the quadratic formula, \( b^2 - 4ac \), that tells you the number of real solutions.
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Systems of Equations