2.2 Solving Quadratic Equations Algebraically

2.2 Solving Quadratic Equations Algebraically - Solving...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Solving Quadratic Solving Equations Algebraically Equations Section 2.2 Defn. of Quadratic Equation Defn. A quadratic or second degree, equation is one that can be written in the form: ax + bx + c = 0, a ≠ 0 2 The Zero Product Property The If a product of real numbers is zero, then at least one of the factors is zero. If ab = 0, then a = 0 or b = 0 (or both) Completing the Square Completing To complete the square of the expression x 2 + bx , add the square of one­half the coefficient of x, namely . b 2 ÷ 2 The addition produces a perfect square trinomial. 2 2 b b x + bx + ÷ = x + ÷ 2 2 2 Solve by completing the square. 2x − 6x +1 = 0 2 2 x − 6 x = −1 subtract 1 1 2 x + 3 x + ___ = − + ___ 2 Divide by 2 2 9 19 x − 3x + = − + Add half of 3 squared 4 24 2 2 3 7 Rewrite as perfect x− ÷ = 2 4 square and simplify 3 7 x− =± 2 2 The Quadratic Formula The The solutions of the quadratic equation 2 are ax + bx + c = 0 −b ± b − 4ac x= 2a 2 The Discriminant The Discriminant Value Number of Real Solutions b − 4ac > 0 2 distinct real solutions b − 4ac = 0 1 distinct real solution 2 2 b − 4ac < 0 2 0 real solutions Joke Time Joke What do you get if Batman and Robin get smashed by a steam roller? Flatman and ribbon What kind of car does Luke Skywalker drive? A toy­yoda ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online