Translation of a graph and its vertex

Practise translation of a graph and its vertex with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

The graph $y=x^2$ is translated 3 units right and 2 units down. (a) Write the transformed equation. [2 marks] (b) State the vertex and range. [2 marks]

Worked explanation

• Part (a)

  A translation right by 3 replaces x with $x-3$; down by 2 subtracts 2 from the output.

• Part (b)

  The squared term is nonnegative and is zero at $x=3$. Thus the vertex is $(3,-2)$ and the least output is $-2$.

(a) $y=(x-3)^2-2$.; (b) $(3,-2)$; $[-2,\infty)$.

Original VectorPaths practice; not an official VCAA question or marking rubric.