<s>[INST] Solving quadratic equations by completing the square. 
Graphing $y=ax^2+ bx + c$ by completing the square

*

*Add and subtract the square of half the coefficent of $x$.


*Group the perfect square trinomial.


*Write the trinomial as a square of a binomial.
Rewrite $y = x^2 + 6x + 8$ into $y = a(x-h)^2 + k$.

I've tried solving this but I get a bit confused at the step where I have to "write the trinomial as a square of a binomial". Not exactly sure how to do that.
 [/INST] To complete the square for the equation:
$y = x² + 6x + 8$
Start by: 
1) $x^2+6x+8$
2) $x^2+\dfrac 62x +8$ *divide the bx by 2
3) $(x^2+\dfrac 62x + (\dfrac 62)^2)+8$ *square the bx term to form a perfect square
4) $(x^2+ 3x + (36/4))+8$
5) $(x^2+3x + 9)+8-9$ *add the inverse of the c term
6) $(x^2+3x+9)-1$ *factor the perfect square
7) $(x+3)^2-1$
8) $y=(x+3)^2-1$
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