Following IB DP Math A&A SL book Oxford Course Companion p. 131ff.
You can transform the parent graph [math]f\left(x\right)=x^2[/math] to the graph of any other parabola [math]y=g\left(x\right)[/math] 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.