# 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 [latex]x[/latex]-intercepts, are the points at which the parabola crosses the [latex]x[/latex]-axis. The [latex]y[/latex]-intercept is the point at which the parabola crosses the [latex]y[/latex]
*-*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 [latex]y[/latex]-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 [latex]x[/latex] at which [latex]y=0[/latex], also called roots

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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].