transforming a parabola

Practise transforming a parabola with an original VectorPaths question, worked explanation and related VCE Methods practice.

3 practice marks

Original practice question

The graph of $y=x^2$ is transformed into $y=5 - 2 \left(x - 3\right)^{2}$. State the transformations, the vertex and the range.

Worked explanation

• Read the transformations

  Stretch vertically by factor 2, and reflect in the x-axis. Translate horizontally by 3 and vertically by 5 (signed distances).

• Find the vertex

  The squared term is zero at $x=3$, giving vertex $(3,5)$.

• Use the opening direction

  The coefficient is -2, so the range is $(-\infty,5]$.

Vertex $(3,5)$; range $(-\infty,5]$.

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