# 10.1: Quadratic Functions and Their Graphs

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**Practice**Quadratic Functions and Their Graphs

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-intercept of a parabola

As with linear equations, the**of a parabola are where the graph intersects the -axis. The -value is zero at the**

*-intercepts***.**

*-intercepts*leading coefficient of a parabola

The variable in the equation is called the**of the quadratic equation.**

*leading coefficient*minimums and maximums of a parabola

An equation of the form forms a parabola. If is positive, the parabola will open**The vertex will be a**

*upward.***If is negative, the parabola will open**

*minimum.***The vertex will be a**

*downward.*

*maximum.*symmetry of a parabola

A parabola can be divided in half by a vertical line. Because of this, parabolas have**. The vertical line dividing the parabola into two equal portions is called the line of**

*symmetry***.**

*symmetry*vertex of a parabola

All parabolas have a**, the ordered pair that represents the bottom (or the top) of the curve. The line of symmetry always goes through the vertex. The**

*vertex***is the ordered pair .**

*vertex of a parabola*Coefficient

A coefficient is the number in front of a variable.Dilation

To reduce or enlarge a figure according to a scale factor is a dilation.domain

The domain of a function is the set of -values for which the function is defined.Horizontal shift

A horizontal shift is the result of adding a constant term to the function inside the parentheses. A positive term results in a shift to the left and a negative term in a shift to the right.Parabola

A parabola is the characteristic shape of a quadratic function graph, resembling a "U".quadratic function

A quadratic function is a function that can be written in the form , where , , and are real constants and .standard form

The standard form of a quadratic function is .Symmetry

A figure has symmetry if it can be transformed and still look the same.Vertex

The vertex of a parabola is the highest or lowest point on the graph of a parabola. The vertex is the maximum point of a parabola that opens downward and the minimum point of a parabola that opens upward.vertical axis

The vertical axis is also referred to as the -axis of a coordinate graph. By convention, we graph the output variable on the -axis.### Image Attributions

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Description

Learn the anatomy of the graph of a quadratic function.

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Difficulty Level:

Basic
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Date Created:

Feb 24, 2012
Last Modified:

Aug 08, 2016
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