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11: Quadratic Equations and Applications

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    Learning Objectives

    By the end of this chapter, the student should be able to

    • Solve quadratics by the square root property, completing the square, and using the quadratic formula
    • Graph a quadratic function by using properties or transformations
    • Solve quadratic inequalities by graphing, or algebraically
    • Find the extreme value of a quadratic function
    • Solve applications and functions using quadratic functions

    We might recognize a quadratic equation from the factoring chapter as a trinomial equation. Although, it may seem that they are the same, they aren’t the same. Trinomial equations are equations with any three terms. These terms can be any three terms where the degree of each term can vary. On the other hand, quadratic equations are equations with specific degrees on each term.

    Definition: Quadratic Equation

    A quadratic equation is a polynomial equation of the form


    where \(ax^2\) is called the leading term, \(bx\) is called the linear term, and \(c\) is called the constant coefficient (or constant term). Additionally, \(a\neq 0\).

    In this chapter, we discuss quadratic equations and its applications. We learn three techniques for solving quadratic equations:

    • Square root property
    • Completing the square
    • Quadratic Formula

    Recall, we also have the technique of factoring. After this chapter, we solve quadratic equations by using any of the techniques we have discussed in this textbook. The first technique is using the Square root property.

    This page titled 11: Quadratic Equations and Applications is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Darlene Diaz (ASCCC Open Educational Resources Initiative) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.