Variation 1 · answer guide

Graph transformations — Simple translated absolute value

Question

The graph with vertex opening upwards with slope has equation

This practice question was inspired by Question 8 in the 2023 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Set up the solution: track how each transformation moves key points, asymptotes and intercepts of the base graph.Vertex form with gives .
Finish the calculation, then check that the result meets the question’s conditions.Option D opens downwards.
Match the result to the choices and state the correct option.Therefore option A is correct.

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: At , ; at , .

Any mark labels are a TestMum study aid, not an official NESA marking allocation.