Translations
shifts UP. shifts LEFT (sign flips for horizontal).
Vertical translation: .
- Adds to every -value.
- Graph moves UP by (or DOWN if negative).
Example. .
- . Vertex moves from to . Up by .
- . Vertex at . Down by .
Horizontal translation: .
- Replaces with INSIDE the function.
- Graph moves LEFT by (counter-intuitive!).
- moves RIGHT by .
Example. .
- . Vertex at . LEFT by .
- . Vertex at . RIGHT by .
Why does horizontal translation work backwards?
Think: 'where is in the new graph?' For : at , i.e. . So the value originally at is now at . Graph shifted LEFT.
Combined translation.
: shift LEFT by AND UP by .
Vector notation: translation by .
Worked qualitative. Sketch .
- This is translated by .
- Vertex at .
- Up-opening parabola.
Edexcel tip. Always state translation as a VECTOR. Mark schemes credit the explicit vector.
- : UP by .
- : LEFT by (counter-intuitive).
- : RIGHT by .
- Vector: for .