Building the Perfect Square

Learning Focus

Complete the square using an area-model / perfect-square trinomial idea.

Big idea

For $x^2+bx$, take half of $b$, square it, and add that to build $(x+\frac{b}{2})^2$.

Example: $x^2+8x$ needs $+16$ because $(\frac{8}{2})^2=16$, giving $(x+4)^2$.

Takeaways

• Completing the square rewrites standard form into vertex form.
• Balance the equation: if you add a number, also subtract it (or add to both sides).