The function is quadratic equation, more precisely a standard form equation such as : y= ax^2 +bx+c
When the variable "a",which is the slope of the equation, it changes its form, by that I mean, it shrinks or it stretches, these changes depend on wheater "a" is greater or less then 0. The variable "b" can either shift horizontally or vertically. The variable "c" affects the vertical shift of the graph. Meaning, that if "c" is negative it is lowered, if "c" is positive it is higher in the graph.