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Chapter 19.2
Transformations of quadratic functions
What You'll Learn
Identify how coefficients and constants transform the parent function y = x²
Apply reflection transformations across the x-axis using negative coefficients
Perform vertical stretches and compressions by multiplying y-values
Execute horizontal and vertical translations by modifying x and y terms
Determine the vertex of a transformed parabola from its equation
Combine multiple transformations to graph complex quadratic functions
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
Skills
Quadratic Functions
Transformations
Vertex Form
Reflections
Translations
Vertical Stretch
Horizontal Shift
Graphing Parabolas
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