This worksheet allows you to investigate how the constants a, h and k affect the appearance of a parabola whose equation is written in Vertex form. It may take a minute for the GeoGebra applet below to load, so please be patient (and give it permission to load if you receive any warnings from your browser)

Drag the points a, M, and N along their sliders and see what happens. Can you:
- Make the curve go through the origin?
- Make the curve go through the point (-3,-1)?
- Make the curve have a wider opening?
- Make the curve have a narrower opening?
- Make the curve open sideways?
- Make the curve open down instead of up?
- Make the curve into a line?
Which of the above could NOT be achieved? Why not?