Quadratic Functions
Quadratic Functions are functions of the specific form
As long as you have an x-squared term and an x term and a constant, the coefficients a, b and c can be any number.
The Quadratic Formula
The Quadratic Formula can be used to factor and solve for the roots of a quadratic function. To use it, plug a, b and c into the Quadratic Formula, here:
If any terms in your quadratic function are negative, make sure to keep the negative sign when plugging into the formula. For example, if b is negative in your quadratic function, you’ll end up with –(-b) for the first term in the numerator of the Quadratic Formula, which would make that term positive.
You should also remember that in order for this formula to work, the value under the square root sign must be greater than or equal to zero, because you can’t take the square root of a negative number. If you do end up with a negative number inside the radical, then there are no real solutions to your quadratic function.
Review the example on the left. Since you always get a fraction with a plus or minus sign in the numerator, the Quadratic Formula produces two solutions, which you then use to factor your polynomial. If your solutions are r and r1, your factors will always be (x-r) and (x-r1).
