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
- 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
Glossary
- 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
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- Revision and Adaptation. Provided by: Lumen Learning License: CC BY: Attribution.
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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].