A quadratic equation is any equation involving any quadratic form: standard, vertex, etc. The most common is \(ax^2+bx+c=0\). One KEY POINT here, in order to solve, the equation MUST be set equal to \(0\). This may require some up front algebra to rearrange the equation and set it equal to zero. The goal is to find values of \(x\) that make the equation true. Most quadratic equations will have two solutions, however, having exactly one solution or no solutions are also possibilites.
One method used to help solve quadratic equations is factoring. When the trinomial can be factored, this method provides quick steps to getting to the solutions. The factoring portion does not provide the answer, one extra step needs to happen. Setting each binomial factor equal to zero
Recall the vertex-form of a quadratic function: \(f(x)=a(x-h)^2+k\). When this is put into an equation, the following video will show methods of solving these types of equations.
Here are a few more worked out examples. Try first on your own, then click on the button for the solutions
| \(w^2+8w-48=0\) | \(7n^2+53n=24\) | \(5z^2-9=151\) |
|---|---|---|