FUN017 · Functions & graphs · Classes 11–12
Transformations of graphs
A graph can be shifted, stretched and reflected. In a·f(x − h) + k: h moves it right, k moves it up, a stretches it (and flips it if negative).
af(x − h) + kTransformations of graphs
📐 Formula
y = a·f(x − h) + k
✏️ Worked example
y = (x − 2)² − 3 is y = x² (grey) moved 2 right and 3 down: vertex (2, −3).
🌍 Where it is used
Fitting a model to data; animation and graphics.
❓ Quick check
y = x² + 4 is y = x² moved…
🏋️ Practice
EasyVertex of y = (x + 1)² + 2?
Answer: (−1, 2)
Mediumy = −x² is y = x² …?
Answer: reflected in the x-axis
ChallengeWrite y = x² moved 3 left and 1 down.
Answer: y = (x + 3)² − 1