Following IB DP Math A&A SL book Oxford Course Companion p. 131ff.
You can transform the parent graph to the graph of any other parabola by applying one or more of four basic transformations.
Try to find the changes to the parent graph by modifying the parent function equation:
g is a vertical stretch with scale factor 2. If the scale factor is 0<a<1, then g is a vertical compression. For negative scale factors, g is a reflection about the x-axis.
All transformations combined form the "vertex form" of a parabola, where (h,k) are the coordinates of the vertex.