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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 10-7 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 x-intercepts One double (repeated) real roots x-intercept No real roots no x-intercept Exercise 1.1 P.8 Nature of Roots △...
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