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10.1: Quadratic Functions and Their Graphs

Difficulty Level: Basic Created by: CK-12
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x-intercept of a parabola

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

leading coefficient of a parabola

The variable a in the equation y=ax^2+bx+c is called the leading coefficient of the quadratic equation.

minimums and maximums of a parabola

An equation of the form y=ax^2+bx+c forms a parabola. If a is positive, the parabola will open upward. The vertex will be a minimum. If a is negative, the parabola will open downward. The vertex will be a maximum.

symmetry of a parabola

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

vertex of a parabola

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


A coefficient is the number in front of a variable.


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


The domain of a function is the set of x-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.


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 f(x)=ax^2 + bx + c, where a, b, and c are real constants and a\ne 0.

standard form

The standard form of a quadratic function is f(x)=ax^{2}+bx+c.


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


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 y-axis of a coordinate graph. By convention, we graph the output variable on the y-axis.

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Difficulty Level:
8 , 9
Date Created:
Feb 24, 2012
Last Modified:
Aug 08, 2016
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