Porisma

Worked solution

Move the parabola vertically

Use a graphing calculator to sketch:

  1. y=x2y=x^2
  2. y=x2+1y=x^2+1
  3. y=x2−2y=x^2-2

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

CJC · Transformations · Vertical translation activity

Sketch the three curves

Answer

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

Plot the three equations together. Each has symmetry axis x0 and the same quadratic shape. The Teacher fills the two new minimum coordinates and labels the curves; those observation coordinates are blank in the Student copy.

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

Describe the vertical translations

Answer

Shape and size are preserved; move up 1 or down 2.

Replace y with y−1y-1: y−1=x2y-1=x^2, hence y=x2+1y=x^2+1, a translation 1 unit in the positive y-direction. Replace y with y+2y+2: y+2=x2y+2=x^2, hence y=x2−2y=x^2-2, a translation 2 units in the negative y-direction. The original minimum moves from (0,0)(0,0) to (0,1)(0,1) or (0,−2)(0,-2).

How did this part go?