#### Answer

See table P5 "Determining the Most Efficient Technique to Use when Solving a Quadratic Equation"
(sample answer follows)
The given equation is $ ax^{2}+bx+c=0$.
First, see if a term is missing, $ bx $ or $ c.$
The factoring (c missing) or square-root property (bx is missing) methods lead to a quick solution.
If not, you look to factor $ ax^{2}+bx+c $.
This is easier when a=1, and slightly more complicated when $ a\neq 1.$
If factoring does not seem easy, maybe the leading coefficient a is a perfect square.
Then, try the complete-the-square method.
If all else fails, we can use the quadratic formula.
We can always use the quadratic formula.

#### Work Step by Step

Given above.