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The correct answer is $7$. When an equation is of the form $y=a{x}^2+bx+c$, where $a$, $b$, and $c$ are constants, the value of $y$ reaches its minimum when $x=-\frac{b}{2a}$. Since the given equation is of the form $y=a{x}^2+bx+c$, it follows that $a=1$, $b=-14$, and $c=22$. Therefore, the value of $y$ reaches its minimum when $x=-\frac{\left(-14\right)}{2\left(1\right)}$, or $x=7$.