Put the equation $y=x^{2}+18 x+72$ into the form $y=(x-h)^{2}+k$ : Answer: $y=$ Question Help:

Step 1 ：The equation \(y=x^{2}+18 x+72\) is in the form of a quadratic equation \(y=ax^{2}+bx+c\). To convert it into the form \(y=(x-h)^{2}+k\), we need to complete the square.

Step 2 ：The general formula for completing the square is \(y=a(x-h)^{2}+k\), where \(h=-\frac{b}{2a}\) and \(k=c-\frac{b^{2}}{4a}\).

Step 3 ：In this case, \(a=1\), \(b=18\), and \(c=72\). So, \(h=-\frac{b}{2a}=-\frac{18}{2*1}=-9\) and \(k=c-\frac{b^{2}}{4a}=72-\frac{18^{2}}{4*1}=72-81=-9\).

Step 4 ：So, the equation in the form \(y=(x-h)^{2}+k\) is \(y=(x+9)^{2}-9\).

Step 5 ：Final Answer: \(\boxed{(x+9)^{2}-9}\)