Earlier in the class, we learned how to solve quadratic equations by factoring. This works fine, as long as we are able to successfully complete the factoring step. For quadratics that cannot be factored, we will need to turn to alternative methods.
There are two methods we will use, the square root property (which is relatively simple, but doesn’t work in all cases), and the quadratic formula (which works for all quadratic equations).
This video gives a basic example of the square root property:
The next video includes several examples, both simple and more complicated, using the square root property:
The quadratic formula is a single formula that allows us to solve any quadratic equation, regardless of whether we can factor it or apply the square root property. It is important when using the quadratic formula to first put the equation in standard form (make it equal to zero), so that you can correctly identify the numbers a, b, and c before plugging in.
Here are two examples of using the quadratic formula to solve a quadratic equation: