y = f(x) + a moves a graph up or down, y = f(x + a) moves it left or right. Points, turning points, equations and vectors.
What you will learn
- Find where a point or turning point moves to under a translation
- Write the equation of a translated graph
- Describe a translation by a column vector
Outside the bracket: up and down
y = f(x) + a adds a to every y value.
The graph moves up a (down if a is negative): a translation by the vector with top 0 and bottom a.
- y = f(x) has a minimum point at (2, −5)
- y = f(x) + 3 has its minimum point at (2, −2)
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Outside the bracket: up and down
- Inside the bracket: the opposite way
- The equation after a translation
- Try it: Slide the curve
7 practice questions, marked as you go; about 25 minutes in all.
Key terms
Up a, Left a, Every
In this unit: Functions and graph transformations
Function notation, composite and inverse functions, the shapes of standard graphs, translations and reflections of y = f(x), and the graphs of sin, cos and tan (Higher).