Given:
[tex] y = \frac{1}{2} {(x - 4)}^{2} + 13[/tex]
simplify the square factor:
[tex]y = \frac{1}{2} ( {x}^{2} - 8x + 16) + 13[/tex]
[tex]y = \frac{1}{2} {x}^{2} - 4x + 8 + 13[/tex]
the solution is then:
[tex]y = \frac{1}{2} {x}^{2} - 4x + 21[/tex]
