Porisma

Worked solution

Move the parabola horizontally

Use a graphing calculator to sketch:

  1. y=x2y=x^2
  2. y=(x+1)2y=(x+1)^2
  3. y=(x−2)2y=(x-2)^2

Copy the curves. What do you observe about the curves?

CJC · Transformations · Horizontal translation activity

Sketch the three curves

Answer

Upward parabolas with vertices (0,0)(0,0), (−1,0)(-1,0) and (2,0)(2,0).

Plot all three on the same axes. The Teacher labels the shifted vertices and the two translated equations; the Student has the curves but leaves those observation coordinates blank. A graphing calculator can display the three entries together; no further key sequence is specified on this page.

Expand diagram

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Three equal-sized upward parabolas x²,(x+1)²,(x−2)² with labelled vertices (0,0),(−1,0),(2,0).
Three equal-sized upward parabolas x²,(x+1)²,(x−2)² with labelled vertices (0,0),(−1,0),(2,0).
Three equal-sized upward parabolas x²,(x+1)²,(x−2)² with labelled vertices (0,0),(−1,0),(2,0).
How did this part go?

Describe what is preserved and what moves

Answer

Shape and size are preserved; the vertex moves left 1 or right 2.

Replacing xx by x+1x+1 gives a translation 1 unit in the negative x-direction. Replacing it by x−2x-2 gives a translation 2 units in the positive x-direction. Thus the original minimum (0,0)(0,0) becomes (−1,0)(-1,0) or (2,0)(2,0) respectively. Both are rigid translations, so the shape and size stay unchanged.

How did this part go?