The vertex of a parabola lies on the axis of symmetry which divides the parabola into two mirror images. Notice that the two points are reflection of each other about a vertical line since they have the same yy-coordinate. This means that the average of their xx-coordinates is the xx-coordinate of the vertex:

\(\displaystyle{x}=\frac{{−{1}+{5}}}{{2}}={2}\)

To find the y-coordinate of the vertex, substitute x=2 to the equation:

\(\displaystyle{y}={4}{\left({2}\right)}^{{2}}−{16}{\left({2}\right)}+{21}={5}\)

So, the vertex is at:

(2,5)

\(\displaystyle{x}=\frac{{−{1}+{5}}}{{2}}={2}\)

To find the y-coordinate of the vertex, substitute x=2 to the equation:

\(\displaystyle{y}={4}{\left({2}\right)}^{{2}}−{16}{\left({2}\right)}+{21}={5}\)

So, the vertex is at:

(2,5)