Algebra/Chapter 9/Quadratic Equation

Algebra Quadratic Equation Completing the Square Binomial Theorem Derivation The solutions to the general-form quadratic function can be given by a simple equation called the quadratic equation. To solve this equation, recall the completed square form of the quadratic equation derived in the previous section: In this case, since we're looking for the root of this function. To solve, first subtract c and divide by a: Take the (plus and minus) square root of both sides to obtain: Subtracting from both sides: This is the solution but it's in an inconvenient form. Let's rationalize the denominator of the square root: Now, adding the fractions, the final version of the quadratic formula is: This formula is very useful, and it is suggested that the students memorize it as soon as they can. Discriminant The part under the radical sign, , is called the discriminant, . The value of the discriminant tells us some useful information about the roots. If , there are two unique real solutions. If , there is one unique real solution. If , there are two unique, conjugate imaginary solutions. If is a perfect square then the two solutions are rational, otherwise they are irrational conjugates. Word Problems Need to pull word problems from http://teachers.yale.edu/curriculum/search/viewer.php?id=initiative_07.06.12_u&skin=h