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
