To express a quadratic function of the form [tex]a x^{2} +bx+c[/tex] into its vertex form [tex]a(x-p)=q[/tex] (p and q are integers), we are going to use the completing square method: Step 1 Add 1 to both sides of the equation: [tex]x^2+6x+8=0[/tex] [tex]x^2+6x+8+1=0+1[/tex] Step 2 Perform the operations: [tex]x^2+6x+9=1[/tex] Step 3 Notice that [tex]9=3*3=3^2[/tex], so we can rewrite our expression as follows: [tex]x^2+6x+3^2=1[/tex] [tex](x+3)^2=1[/tex]
We can conclude that the correct steps to transform x2 + 6x + 8 = 0 into the form (x − p)2 = q [p and q are integers] are: B. Step 1 x2 + 6x + 8 + 1 = 0 + 1 Step 2 x2 + 6x + 9 = 1 Step 3 (x + 3)2 = 1