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TMUA 2020 · Paper 1 · Question 10 of 20

TMUA 2020 Paper 1 Question 10

Graphs and transformations — Transformations · applying a sequence in order. Try it first; the answer and a full worked solution are below.

TMUA 2020 · Paper 1Graphs and transformationsTransformations · applying a sequence in order8 options
The following sequence of transformations is applied to the curve y = 4x2:

1.  Translation by (3−5)
2.  Reflection in the x-axis
3.  Stretch parallel to the x-axis with scale factor 2

What is the equation of the resulting curve?

  1. Ay = −x2 + 12x − 31
  2. By = −x2 + 12x − 41
  3. Cy = x2 + 12x + 31
  4. Dy = x2 + 12x + 41
  5. Ey = −16x2 + 48x − 31
  6. Fy = −16x2 + 48x − 41
  7. Gy = 16x2 − 48x + 31
  8. Hy = 16x2 − 48x + 41
Show the answer and worked solution
answer · A
  1. Ay = −x2 + 12x − 31
  2. By = −x2 + 12x − 41
  3. Cy = x2 + 12x + 31
  4. Dy = x2 + 12x + 41
  5. Ey = −16x2 + 48x − 31
  6. Fy = −16x2 + 48x − 41
  7. Gy = 16x2 − 48x + 31
  8. Hy = 16x2 − 48x + 41
Apply them one at a time. The translation gives y = 4(x−3)2 − 5. Reflecting in the x-axis negates the whole right-hand side: y = −4(x−3)2 + 5. A stretch parallel to the x-axis with scale factor 2 replaces x by x2, giving y = −4(x2 − 3)2 + 5 = −(x−6)2 + 5. Expanding gives y = −x2 + 12x − 31. Replacing x by 2x instead of x2 leads to the −16x2 options.