Rucete ✏ Mathematics In a Nutshell
Translation of Parabolas
If you read Translation of Functions, you will understand better.
Vertical Translation
y = f(x) + a
Moves the graph vertically by a units.
Example
y = x² + 2
Vertex (0 , 2)
→ Shift the graph vertically by 2 units
Horizontal Translation
y = f(x+a)
shift the graph horizontally by -a units
Example
y = (x - 2)²
Vertex (2 , 0)
→ Shift the graph horizontally by 2 units
Example
y=(x-2)² + 2
Vertex (2 , 2)
→ Shift the graph vertically and horizontally by +2 units