Déterminer les formes canoniques de chacun des polynômes de degré 2 suivants. •f(x) = x² - 4x - 3 •g(x) = 2x² - 8x 1 •i(x)=x²-x •h(x) = 2x² + 3x+1 •k(x) = -3x²

Bonjour

f(x) = x² - 4x - 3

= x² - 4x + 4 - 3 - 4

= (x-2)²- 7

g(x) = 2x² - 8x + 1 = 2(x²- 4x + 1/2)

= 2( (x-2)² - 2² +1/2) ) = 2( (x-2)² - 7/2 )

= 2(x-2)² - 7

i(x) = x² - x = (x-1/2)² - (1/2)² = (x-1/2)² - 1/4

k(x) = -3x² + 5x + 2 = -3(x² - 5/3 x - 2/3) = -3( (x - 5/6)² - (5/6)² - 2/3 )

= -3( (x-5/6)² - 49/36 ) = -3(x-5/6)² + 49/12

j(x) = 4x² - 3 = 4(x² - 3/4) = 4( (x-3/8)² - (3/8)² )

= 4(x-3/8)² - 9/16