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MathAlgebra

Horizontal Stretch: Transform x² by Factor 3, Left 4, Down 3

Apply a horizontal stretch of factor 3 to x², then shift left 4 and down 3. Derive g(x) = ((x + 4)/3)² − 3 and check the transformed vertex.

Question

Start with the graph of f(x)=x2f(x)=x^2. Apply these changes in order: stretch horizontally by factor 3, translate 4 units left, and translate 3 units down. Write the resulting function gg.

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Evidence boundary

This page solves OpenStax College Algebra 2e, Section 3.5, Exercise 68. The order is horizontal stretch, then left translation, then downward translation. The formula and coordinate checks are derived here; no diagram or empirical measurement is needed to determine the result.