Overview
Watch
Read
Next Steps
Overview
Advanced Mathematics 2200
Relations and Functions
6. NL.SO.2200RF3
6.1 Characteristics of quadratic functions
Characteristics of Quadratic Functions
Understand the parabola shape, vertex, axis of symmetry, intercepts, domain, and range that define every quadratic function.
What You'll Learn
A quadratic function always graphs as a parabola, a symmetric U-shaped curve.
The sign of the leading coefficient tells you whether the parabola opens upward or downward.
The vertex is the highest or lowest point on the graph, and the axis of symmetry passes through it.
X-intercepts show where the function equals zero, and the y-intercept shows the value when x equals zero.
Every quadratic function has domain of all real numbers, but its range depends on the direction the parabola opens.
What You'll Practice
1
Finding vertex coordinates from parabola graphs
2
Determining whether parabolas open upward or downward
3
Calculating x-intercepts and y-intercepts algebraically
4
Writing equations for axis of symmetry
5
Identifying domain and range from graphs
Why This Matters
Understanding the characteristics of quadratic functions gives you the foundation to analyze parabolas in physics, engineering, and economics. Whether you're modeling projectile motion, profit curves, or optimization problems, recognizing how vertex, domain, and range work together is essential for success in advanced math and STEM careers.
Before You Start — Make Sure You Can:
This Unit Includes
10 Video lessons
Learning resources
Skills
Parabola
Vertex
Domain and Range
Axis of Symmetry
Intercepts
End Behavior
Quadratic Functions
NL Curriculum Aligned