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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
ON Curriculum Aligned