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'Geometric Parabola' printed from https://nrich.maths.org/
$$y=ax^2+2bx+c$$
Start with $a=1, b=2, c=4$ - what does the graph look like? What
key points does it pass through?
Then try $a=2, b=4, c=8$, $a=4, b=8, c=16$ and so on. Look for
similarities and differences between the graphs.