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 $y=3 \left(x + 1\right)^{2} - 4$. State the transformations, the vertex and the range.

Worked explanation

• Read the transformations

  Stretch vertically by factor 3. Translate horizontally by -1 and vertically by -4 (signed distances).

• Find the vertex

  The squared term is zero at $x=-1$, giving vertex $(-1,-4)$.

• Use the opening direction

  The coefficient is 3, so the range is $[-4,\infty)$.

Vertex $(-1,-4)$; range $[-4,\infty)$.

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