This document discusses exploring properties of quadratic functions through investigating different forms of expression and transformations of quadratic graphs. It examines exploring properties like the vertex and line of symmetry for basic quadratic functions like y=x^2 as well as transformed functions like y=(x-h)^2, looking at shifts along the x-axis and y-axis. Examples are provided of sketching graphs for quadratic functions in different forms and with different transformations, concluding with identifying the vertex and line of symmetry for general quadratic functions of the form y=a(x-h)^2+k.