Use when:
1. you are told to solve by factoring.
Such as: "Solve by factoring".
2. the quadratic is easily factorable.
Such as: x^{2}  4x  12 = 0
3. the quadratic is already factored.
Such as: (x + 5)(x  8) = 0
4. the constant term, c, is missing.
Such as: 3x^{2}  x = 0 
Use when:
1. you are told to solve by square root method. Such as: "Solve by square root method".
2. x^{2} is set equal to a numeric value.
Such as: x^{2} = 9 or x^{2} = 12
3. the middle term, bx, is missing.
Such as: 3x^{2}  15 = 0
4. you have the difference of two squares.
Such as: x^{2}  81 = 0 
Use when:
1. you are told to solve by completing the square.
Such as: "Solve by completing the square".
2. you are told to put the quadratic into vertex form, a(x  h)^{2} + k = 0, before solving. 
Use when:
1. you are told to use the quadratic formula.
Such as: "Solve by the quadratic formula".
2. factoring looks difficult, or you are having trouble finding the correct factors.
Such as: 10x^{2}  3x  4 = 0
3. the quadratic is not factorable.
Such as: x^{2}  6x + 2 = 0
4. the question asks for the answers to form
ax^{2} + bx + c = 0 to be rounded.
Such as: 2x^{2} + 18x + 4 = 0
5. the question asks for the answers to be written in a+bi form.
Such as: x^{2}  6x + 2 = 0

Using a graph to determine the roots (xintercepts) of a quadratic equation may prove to be a difficult process. If you are graphing by hand, it may be hard to find the exact xintercepts (the roots), especially when the xintercepts are not integer values. If you must rely on graphing to solve a quadratic equation, use a graphing utility with the capability of finding the decimal values (or approximations) of the the xintercepts or (zeros).
Remember, if your graph does not cross the xaxis, you will be dealing with complex roots and you must use a different method to find those roots.
Use when:
1. the graph (and table/chart) of the accompanying quadratic function easily shows integer values for the xintercepts.
2. you have a graphing utility with the capability of finding the decimal values (or approximations) of the roots (zeros). 