funkcja y = - x^2 + 2x + 3 delta Δ = b² - 4 a c ; a = - 1 ; b = 2 ; c = 3 Δ = 2² - 4 * ( -1 ) * 3 = 16 ; pierwiastek z delty √Δ = 4 x 1 = -b + √Δ / 2 a ; x 1 = ( - 2 + 4 ) / 2*( - 1 ) = 2/ - 2 = -1 x 1 = - 1 `````````````````````` x 2 = ( - 2 - 4 ) / ( - 2 ) = - 6 / - 2 = 3 x 2 = 3 `````````````` ; x 1 = - 1 ; x 2 = 3 `````````````````````````````````````````````` Teraz znajdziemy wierzchołek paraboli W x = -b / 2 a ; W x = -2 / - 2 = 1 W y = - Δ / 4 a ; W y = - 16 / 4 * ( - 1 ) = - 16 / - 4 = 4 wierzchołek ma współrzędne W = ( 1 , 4 ) `````````````````````````````````````````````````````````````````` postać iloczynowa y = a ( x - x 1) ( x - x 2 ) ; x 1 = - 1 to - x 1 = +1 oraz x 2 = 3 to - x 2 = - 3 dlatego y = - ( x + 1 ) ( x - 3 ) ```````````````````````````````````````````````` postać kanoniczna y = a ( x - p )² + q ; ale p = - b / 2 a czyli tak jak W x = 1 q = - Δ / 4 a czyli tak jak W y = 4 czyli p = 1 ; q = 4 podstawiamy za p oraz q a także za a odpowiednie liczby ; a = -1 ; - p = - 1 ; q = 4 i otrzymujemy y = - ( x - 1 )² + 4 `````````````````````````````` załącznik ; wykres.
