# Summary: Graphs of Quadratic Functions

## Key Equations

general form of a quadratic function | [latex]f\left(x\right)=a{x}^{2}+bx+c[/latex] |

standard form of a quadratic function | [latex]f\left(x\right)=a{\left(x-h\right)}^{2}+k[/latex] |

## Key Concepts

- A polynomial function of degree two is called a quadratic function.
- The graph of a quadratic function is a parabola. A parabola is a U-shaped curve that can open either up or down.
- The axis of symmetry is the vertical line passing through the vertex.
- Quadratic functions are often written in general form. Standard or vertex form is useful to easily identify the vertex of a parabola. Either form can be written from a graph.
- The vertex can be found from an equation representing a quadratic function.
- The domain of a quadratic function is all real numbers. The range varies with the function.

## Glossary

**axis of symmetry**- a vertical line drawn through the vertex of a parabola around which the parabola is symmetric; it is defined by [latex]x=-\frac{b}{2a}[/latex].

**general form of a quadratic function**- the function that describes a parabola, written in the form [latex]f\left(x\right)=a{x}^{2}+bx+c[/latex], where [latex]a[/latex], [latex]b[/latex], and [latex]c[/latex] are real numbers and [latex]a\ne 0[/latex].

**standard form of a quadratic function**- the function that describes a parabola, written in the form [latex]f\left(x\right)=a{\left(x-h\right)}^{2}+k[/latex], where [latex]\left(h,\text{ }k\right)[/latex] is the vertex.

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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].