If you have a general quadratic equation like this:
The quadratic formula
Practice using the formula now.
- is the coefficient in front of , so here (note that can’t equal -- the is what makes it a quadratic).
- is the coefficient in front of the , so here .
- is the constant, or the term without any next to it, so here .
What does the solution tell us?
Second worked example
There are many more worked examples in the videos to follow.
Tips when using the quadratic formula
- Be careful that the equation is arranged in the right form: or it won’t work!
- Make sure you take the square root of the whole , and that is the denominator of everything above it
- Watch your negatives: can’t be negative, so if starts as negative, make sure it changes to a positive since the square of a negative or a positive is a positive
- Keep the and always be on the look out for TWO solutions
- If you use a calculator, the answer might be rounded to a certain number of decimal places. If asked for the exact answer (as usually happens) and the square roots can’t be easily simplified, keep the square roots in the answer, e.g. and
- Watch Sal do an example:
- Prove the quadratic formula: