This is an example of a Quadratic Equation. Quadratic equations are in the form of y=ax^2+bx+c. Each variable in this equation has the ability to change different factors about the graph, including the width, vertical shift, and horizontal shift.
a in this equation controls the width of the graph, as a increases the width decreases, as a decreases, the graph gets wider. When a is smaller than 0 the graph is reflected over the x-axis.
b in this equation is basically the horizontal shift.
c in this equation is the vertical shift for the graph.