Skip Navigation

10.1: Quadratic Functions and Their Graphs

Difficulty Level: Basic Created by: CK-12
Atoms Practice
This indicates how strong in your memory this concept is
Practice Now
This indicates how strong in your memory this concept is
Turn In

Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Show More


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

Image Attributions

Show Hide Details
Difficulty Level:
8 , 9
Date Created:
Feb 24, 2012
Last Modified:
Aug 08, 2016
Save or share your relevant files like activites, homework and worksheet.
To add resources, you must be the owner of the Modality. Click Customize to make your own copy.
Please wait...
Please wait...
Image Detail
Sizes: Medium | Original