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Section 1.9 Summary of Solving Quadratic Equations

Subsection 1.9.1 Summary of Solving Quadratic Equations

For a quadratic equation \(ax^2 + bx + c = 0\text{,}\)

  • If there is no \(x\) term, \(ax^2 + c = 0\text{,}\) then solve for \(x^2\text{,}\) and use the square root property. Slightly more generally, if it is in vertex form \((x - h)^2 + k = 0\text{,}\) then use the square root property, and solve for \(x\text{.}\)

  • If \(ax^2 + bx + c\) can be factored easily, then factor and use the zero-product property.

  • If there is no constant term, \(ax^2 + bx = 0\text{,}\) then factor out the common factor of \(x\text{,}\) and use the zero-product property.

  • If \(ax^2 + bx + c\) cannot be factored, or factoring is difficult, then use the quadratic formula.

Technically, the quadratic formula always works, in that is can be used in all cases. However, it is sometimes overkill, applying a complicated formula to a simple situation.

Here is a high-quality math rap song parody, Do the Quad Solve.