This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Quadratic Equations, Quadratic Functions and Absolute Values • 100’s of free ppt’s from www.pptpoint.com library Solving a Quadratic Equation • by factorization • by graphical method • by taking square roots • by quadratic equation • by using completing square By factorization 10 7 2 = + x x ) 2 )( 5 ( = x x 2 _ _ 5 = = x or x 2 _ _ 5 = = x or x roots (solutions) By graphical method 10 7 2 = + x x x y O roots By taking square roots 4 ) 3 2 ( 2 = x 4 3 2 = x 2 3 2 = x 5 2 = x 5 . 2 = x A quadratic equation must contain two roots. ? By taking square roots 4 ) 3 2 ( 2 = x 4 3 2 ± = x 2 3 2 ± = x 1 5 2 or x = 5 . 5 . 2 or x = Solving a Quadratic Equation by the quadratic Formula By quadratic equation , 2 ≠ = + + a c bx ax If a ac b b x 2 4 2 ± = ) 1 ( 2 ) 10 )( 1 ( 4 ) 7 ( ) 7 ( 2 ± = x 10 7 2 = + x x a = b = c = 1 107 2 5 = = x or x In general, a quadratic equation may have : (1) two distinct (unequal) real roots (2) one double (repeated) real root (3) no real roots Two distinct (unequal) real roots xintercepts One double (repeated) real roots xintercept No real roots no xintercept Exercise 1.1 P.8 Nature of Roots △...
View
Full
Document
This note was uploaded on 11/17/2011 for the course PHYS 121 taught by Professor Burgeson during the Fall '11 term at BYU.
 Fall '11
 Burgeson

Click to edit the document details