It is understood the vertex of a parabolic curve described by the quadratic function

is located where

and hence,

. It is insightful to view the location of the vertex as being the intersection point of the line

and the parabola

to better understand how the coefficients

,

,

affect the location of the vertex.
If the linear coefficient

and the constant coefficient

remains fixed while the quadratic coefficient

varies, then you can observe the vertex of the parabola sliding along the line

as the parabola

changes. If the quadratic coefficient

and the constant coefficient

remains fixed while the linear coefficient

varies, then you can observe the vertex of the parabola sliding along the parabola

as the line

changes.