Exercise:
Bringe die folgen quadratischen Funktionen fx in die Scheitelpunktform fx ax-d^ + e bestimme den Scheitelpunkt hat S und die Nullstellen x_. nprvmulticols abclist abc fx x^ - x abc fx x^ + .x abc fx x^ + x abc fx x^ + x abc fx x^ - x abc fx -x^ - x abc fx -x^ + x abc fx -fracx^ -x abc fx x^ - x + abc fx x^ + x - abc fx x^ + x - abc fx .x^ + x - . abc fx frac x^ - frac x + frac abc fx x^ -x + abc fx -x^-x+ abc fx -x^ - x - frac abclist nprvmulticols

Solution:
nprvmulticols abclist abc awfx x^ - x x^ - x + - x-^ - implies hat S- x_x_- x_ quad x_ abc awfx x^ + .x x^ + .x + . - . x+.^ - . implies hat S-.-. x_x_+. x_ quad x_ -. abc awfx x^ + x x^ + x + - x+^ - implies hat S-- x_x_+ x_ quad x_  - abc awfx x^ + x x^ + x + . - . x+.^ - . implies hat S-.-. x_x_+ x_ quad x_ - abc awfx x^ - x x^ - x x^ - x + - x-^ - implies hat S- x_x_- x_  quad x_ abc awfx -x^ - x -x^ + x -x^ + x + - -x+^ + implies hat S- -x_x_ + x_ quad x_ - abc awfx -x^ + x -x^ -x -x^ -x + - -x-^ + implies hat S -x_x_- x_ quad x_ abc awfx -fracx^ -x -fracx^+x -fracx^+x+ - -fracx+^ + frac implies hat Sqty-frac -fracx_x_+ x_ quad x_ - abc awfx x^ - x + x^ - x + - + x-^ + implies hat S &textkeine Nullstellen abc awfx x^ + x - x^ + x + - - x+^ - implies hat S-- x_+^ uf sqrt x_ + pm uf - x_ - pm x_ - quad x_ abc awfx x^ + x - x^ + x - . x^ + x + - -. x+^ - implies hat S-- x_ frac- pm sqrt+  frac- pm sqrt  frac- pm sqrt abc awfx .x^ + x - . .x^ + x -. .x^ + x + - -. .x+^ - implies hat S-- x_ frac- pm sqrt + frac- pm sqrt abc awfx frac x^ - frac x + frac fracqtyx^ - frac x + frac fracqtyx^ - frac x + frac - frac + frac fracqtyx-frac^ + frac implies hat Sqtyfrac frac &textkeine Nullstellen abc awfx x^ -x + qtyx^ - frac x + qtyx^ - frac x + frac - frac + frac qtyx-frac^ + frac implies hat Sqtyfrac frac &textkeine Nullstellen abc awfx -x^-x+ -x^ + x + -x^ + x + . - . + -x+.^ + . implies hat S-.. x_ frac pm sqrt + - frac- mp sqrt abc awfx -x^ - x - frac -qtyx^ + frac x - frac -qtyx+frac^ implies hat Sqty-frac x_ -frac abclist nprvmulticols