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Unformatted text preview: Quadratic Equations, Quadratic Functions and Absolute Values 100s of free ppts 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...
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 Fall '11
 Burgeson

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