1.4 Quadratic Equations

Quadratic Equations The standard form of a Quadratic Equation is (ax squared +bx + c = 0)a,b, and c are real numbersA Quadratic Equation is a second-degree equation

Zero-Factor Property If ab = 0, then a = 0, or b = 0, or they both equal 0

Square Root Property If x squared = k, then x = the positive OR negative square root of kBoth solutions are real if k > 0

Completing the Square If a does not equal 1, divide both sides of the equation by a Rewrite so that the constant is on one side Square 1/2 of the coefficient of x, add this square to each side of the equation Factor the remaining trinomial as a perfect square and combine like terms Use the Square Root Property to complete

Quadratic Formula

The Discriminant is what lies under the radical sign.A positive, perfect square discriminant means that there are 2 rational solutionsA positive, not perfect square discriminant means that there are 2 irrational solutionsA discriminant of 0 means that there is 1 real answerA negative discriminant means that there are 2 imaginary answers