Put the equation $y=x^{2}+18 x+72$ into the form $y=(x-h)^{2}+k$ :
Answer: $y=$
Question Help:
Final Answer: \(\boxed{(x+9)^{2}-9}\)
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: \(\boxed{(x+9)^{2}-9}\)