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Overview
Mathematics 11
Relations and Functions
13. Demonstrate understanding of characteristics of quadratic functions
13.6 Graphing quadratic functions: General form VS. Vertex form
Graphing Parabolas for Given Quadratic Functions
A clear, step-by-step guide to plotting the graph of any quadratic function using its vertex, axis of symmetry, and intercepts.
What You'll Learn
Every quadratic function \(y = ax^2 + bx + c\) graphs as a U-shaped curve called a parabola.
The vertex, axis of symmetry, and direction of opening are the first things to find before plotting.
Using the axis of symmetry to generate mirror-image points makes sketching the curve much faster.
Vertex form makes the vertex obvious, while standard form requires either the vertex formula or completing the square.
Checking the sign of the leading coefficient tells you immediately whether the parabola opens upward or downward.
What You'll Practice
1
Finding y-intercepts from quadratic functions in general form
2
Solving for x-intercepts by factoring or using square roots
3
Calculating vertex coordinates from both general and vertex forms
4
Sketching complete parabola graphs using all critical points
Why This Matters
Graphing parabolas is essential for visualizing quadratic relationships you'll encounter throughout algebra, calculus, and physics. This skill helps you analyze projectile motion, optimize business profits, and understand how changing variables affect outcomes in real-world scenarios.
This Unit Includes
2 Video lessons
Learning resources
Skills
Parabolas
Quadratic Functions
Intercepts
Vertex
Graphing
Factoring
Vertex Form
NS Curriculum Aligned