Transformations of functions: Vertical translations

All You Need in One Place

Everything you need for Year 6 maths and science through to Year 13 and beyond.

Learn with Confidence

We’ve mastered the national curriculum to help you secure merit and excellence marks.

Unlimited Help

The best tips, tricks, walkthroughs, and practice questions available.

0/1
?
Intros
Lessons
  1. An Experiment to Study "Vertical Translations"

    Sketch and compare: (y)=x2\left( y \right) = {x^2}
    VS.
    (y3)=x2\left( {y - 3} \right) = {x^2}
    VS.
    (y+2)=x2\left( {y + 2} \right) = {x^2}
  2. Sketch all three quadratic functions on the same set of coordinate axes.
  3. Compared to the graph of y=x2y = {x^2}:
    • the graph of (y3)=x2\left( {y - 3} \right) = {x^2} is translated "vertically" ________ units _____________.
    • the graph of (y+2)=x2\left( {y + 2} \right) = {x^2} is translated "vertically" ________ units _____________.
0/1
?
Examples
Lessons
  1. Vertical Translations
    Given the graph of y=f(x)y=f(x) as shown, sketch:
    1. y=f(x)8y = f\left( x \right) - 8
    2. y=f(x)+3y = f\left( x \right) + 3
    3. In conclusion:
      (y)(y+8)\left( y \right) \to \left( {y + 8} \right): shift ________ units ______________ \Rightarrow all yy coordinates _____________________________.
      (y)(y3)\left( y \right) \to \left( {y - 3} \right): shift ________ units ______________ \Rightarrow all yy coordinates _____________________________.
      Vertical translations
Topic Notes
?
Vertical translations refer to movements of a graph of a function vertically along the y-axis by changing the y values. So, if y = f(x), then y = (x) + h results in a vertical shift. If h > 0, then the graph shifts h units up; while If h < 0, then the graph shifts h units down.