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← 2022 HSC Extension 1 paper Question 4

Variation 1 · answer guide

Graph transformations — Sum of line and parabola

Question

The graph of is a parabola opening upward with vertex on the -axis. Which pair is consistent?

  1. , (constant)
  2. , (sum zero)
  3. ,
  4. ,

This practice question was inspired by Question 4 in the 2022 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Step by step

  1. Set up the solution: track how each transformation moves key points, asymptotes and intercepts of the base graph. is an upward parabola with vertex .
  2. Finish the calculation, then check that the result meets the question’s conditions.B and D give the zero function; C opens downward.
  3. 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: Add the formulas and match opening direction and vertex.

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

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