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Study Guides > College Algebra

Summary: Analysis of Quadratic Functions

Key Equations

the quadratic formula [latex]x=\frac{-b\pm \sqrt{{b}^{2}-4ac}}{2a}[/latex] The discriminant is defined as [latex]b^2-4ac[/latex]   Key Concepts
  • The zeros, or x-intercepts, are the points at which the parabola crosses the x-axis. The y-intercept is the point at which the parabola crosses the y-axis.
  • The vertex can be found from an equation representing a quadratic function.
  • A quadratic function’s minimum or maximum value is given by the y-value of the vertex.
  • The minium or maximum value of a quadratic function can be used to determine the range of the function and to solve many kinds of real-world problems, including problems involving area and revenue.
  • Some quadratic equations must be solved by using the quadratic formula.
  • The vertex and the intercepts can be identified and interpreted to solve real-world problems.
  • Some quadratic functions have complex roots

Glossary

discriminant
the value under the radical in the quadratic formula, [latex]b^2-4ac[/latex], which tells whether the quadratic has real or complex roots
vertex
the point at which a parabola changes direction, corresponding to the minimum or maximum value of the quadratic function
vertex form of a quadratic function
another name for the standard form of a quadratic function
zeros
in a given function, the values of x at which y = 0, also called roots

Licenses & Attributions

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  • College Algebra. Provided by: OpenStax Authored by: Abramson, Jay et al.. Located at: https://openstax.org/books/college-algebra/pages/1-introduction-to-prerequisites. License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].