Ordered reflection, dilation and translation

Practise ordered reflection, dilation and translation with an original VectorPaths question, worked explanation and related VCE Methods practice.

5 practice marks

Original practice question

Start with $y=x^2$. Reflect in the x-axis, dilate vertically by factor 3, then translate 1 unit left and 4 units up. (a) Write the final rule. [2 marks] (b) Find the maximum and all x-intercepts. [3 marks]

Worked explanation

• Part (a)

  Reflection and vertical dilation give $-3x^2$. Replacing x by $x+1$ shifts left; adding 4 shifts up.

• Part (b)

  The negative square is at most zero, so the maximum is 4. Solve $3(x+1)^2=4$ to obtain $x=-1\pm2/\sqrt3$.

(a) $y=-3(x+1)^2+4$.; (b) Maximum $4$ at $x=-1$; $x=-1\pm2/\sqrt3$.

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