Transformations of functions: Vertical translations

What You'll Learn

Identify how adding or subtracting constants outside a function shifts graphs vertically

Apply the rule that y + h shifts graphs down h units while y - h shifts up h units

Recognize that vertical translations affect y-coordinates only, leaving x-coordinates unchanged

Transform original functions by moving all y-coordinates up or down by a fixed amount

What You'll Practice

Graphing functions after vertical shifts up and down

Rewriting equations to identify vertical translation direction

Plotting transformed points by adding or subtracting from y-coordinates

Verifying shifts by substituting values into translated equations

Why This Matters

Vertical translations are essential for understanding how functions transform in algebra and calculus. You'll use this skill to graph families of functions, model real-world situations where baseline values shift, and build toward more complex transformations in advanced math courses.

Before You Start — Make Sure You Can:

Completing the square Converting from general to vertex form by completing the square Shortcut: Vertex formula Graphing parabolas for given quadratic functions

This Unit Includes

2 Video lessons

Skills

Function Transformations

Vertical Translations

Graphing

Coordinate Plane

y-axis Shifts

Quadratic Functions

OH Curriculum Aligned