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Overview
Grade 11 Applied Mathematics (30S)
Develop algebraic and graphical reasoning through the study of relations
12. Demonstrate understanding of characteristics of quadratic functions
12.2 Transformations of quadratic functions
Transformations of Quadratic Functions
See how shifting, stretching, compressing, and reflecting the parent parabola y equals x squared builds every quadratic graph you will ever sketch.
What You'll Learn
Every quadratic graph is a transformation of the parent function y equals x squared
Vertex form y equals a times the quantity x minus h squared plus k shows the transformations directly through a, h, and k
The value of k shifts the parabola up or down, and h shifts it left or right
The value of a stretches or compresses the parabola vertically and flips it over the x axis when a is negative
Applying shifts and stretches in the correct order lets you graph any quadratic function starting from the parent parabola
What You'll Practice
1
Graphing reflections of parabolas across the x-axis
2
Applying vertical expansions and compressions to quadratic graphs
3
Translating parabolas horizontally and vertically using shifts
4
Combining multiple transformations in a single equation
5
Finding vertex coordinates from transformed quadratic equations
Why This Matters
Transforming quadratic functions is essential for modeling real-world phenomena like projectile motion, profit optimization, and engineering designs. Mastering these transformations gives you the power to quickly sketch and analyze parabolas without plotting dozens of points, a skill you'll use throughout algebra, precalculus, and calculus.
Before You Start — Make Sure You Can:
This Unit Includes
3 Video lessons
Practice exercises
Learning resources
Skills
Quadratic Functions
Transformations
Vertex Form
Reflections
Translations
Vertical Stretch
Horizontal Shift
Graphing Parabolas
MB Curriculum Aligned