Use when:
1. you are told to solve by factoring.
Such as: "Solve by factoring".
2. the quadratic is easily factorable.
Such as: x2 - 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: 3x2 - x = 0 |
Use when:
1. you are told to solve by square root method. Such as: "Solve by square root method".
2. x2 is set equal to a numeric value.
Such as: x2 = 9 or x2 = 12
3. the middle term, bx, is missing.
Such as: 3x2 - 15 = 0
4. you have the difference of two squares.
Such as: x2 - 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: 10x2 - 3x - 4 = 0
3. the quadratic is not factorable.
Such as: x2 - 6x + 2 = 0
4. the question asks for the answers to form
ax2 + bx + c = 0 to be rounded.
Such as: 2x2 + 18x + 4 = 0
5. the question asks for the answers to be written in a+bi form.
Such as: x2 - 6x + 2 = 0
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Using a graph to determine the roots (x-intercepts) 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 x-intercepts (the roots), especially when the x-intercepts 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 x-intercepts or (zeros).
Remember, if your graph does not cross the x-axis, 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 x-intercepts.
2. you have a graphing utility with the capability of finding the decimal values (or approximations) of the roots (zeros). |