When we are given a quadratic expression in the standard form:
[tex]y=ax^2+bx+c[/tex]We can complete the squares to rewrite it as:
[tex]y=a(x+d)^2+e[/tex]Where:
[tex]\begin{gathered} d=\frac{b}{2a} \\ . \\ e=e-\frac{b^2}{4a} \end{gathered}[/tex]The poroblem gives us the quadratic equation:
[tex]y=x^2+6x+11[/tex]Here, we have:
a = 1
b = 6
c = 11
Let's calculate d and e:
[tex]\begin{gathered} d=\frac{6}{2\cdot1}=3 \\ \end{gathered}[/tex][tex]e=11-\frac{6^2}{4\cdot1}=11-\frac{36}{4}=2[/tex]Then, we can rewrite:
[tex]y=1(x+3)^2+2[/tex]Thus, the answer is:
[tex]y=(x+3)^2+2[/tex]