The vertex form of the quadratic function is
[tex]f(x)=a(x-h)^2+k[/tex]Where (h, k) are the coordinates of the vertex point
a is the coefficient of x^2
To find h use this rule
[tex]h=-\frac{b}{2a}[/tex]Where b is the coefficient of x
In our equation
The coefficient of x^2 is 1
a = 1
The coefficient of x is 12
b = 12
[tex]h=-\frac{12}{2(1)}=-\frac{12}{2}=-6[/tex]To find k substitute x by -6 in the equation
[tex]k=(-6)^2+12(-6)+33=36-72+33=-3[/tex]The vertex point is (-6, -3)
Let us substitute a, h, k in the vertex form above
[tex]\begin{gathered} f(x)=1(x--6)^2+(-3) \\ f(x)=(x+6)^2-3 \end{gathered}[/tex]