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Created in gnuplot 4.0 with the following commands:
set parametric
set xrange [-3:10]
set yrange [-10:10]
set trange [-3.2:3.2]
set zeroaxis
set key top left
set xtics 2
set ytics 2
set samples 1000
set terminal svg size 3900 6000 dynamic fsize 120
set output 'Semicubical_parabola.svg'
plot fx(t) = t**2, fy(t) = a*t**3, a = 1.0/3, fx(t), fy(t) lw 10 smooth unique title "a = 1/3", a=1, fx(t), fy(t) lw 10 smooth unique title "a = 1", a=2, fx(t), fy(t) lw 10 smooth unique title "a = 2"
I afterwards tweaked it a tiny bit in Inkscape (because AFAIK, gnuplot works in integer coordinates only, so the image needed to be “supersampled”, and therefore all lines were thin).
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