bonjour,
f (x) = ( x - 5 )² - 9
1) f (x) = x² - 10 x + 25 - 9 = x² - 10 x + 16
f (x) = ( x - 5 - 3 ) ( x - 5 + 3 ) = ( x - 8 ) ( x - 2 )
2 ) f ( 0) = ( 0 - 5 )² - 9 = 25 - 9 = 16
f ( 1) = ( 1 - 5 )² - 9 = 16 - 9 = 7
f ( √3) = ( √3 - 5 )² - 9 = 3 - 10 √3 + 25 - 9 = 19 - 10 √3
f (x) = 0
( x - 8 ) ( x - 2) = 0
x = 8 ou 2 (équation produit nul vue en 3 ème )
f (x) = - 9
( x - 5 ) ² - 9 = - 9
( x - 5 )² - 9 + 9 = 0
( x - 5 )² = 0 ⇔ x = 5
f (x) = 16
( x - 5 )² - 9 = 16
( x - 5 )² - 9 - 16 = 0
( x - 5 )² - 25 = 0
( x - 5 - 5 ) ( x - 5 + 5 ) = 0
( x - 10 ) ( x ) = 0 ⇔ x = 10 ou 0
h (x) = x + 16
f (x) = h ( x )
( x - 5 )² - 9 = x + 16
x² - 10 x + 25 - 9 = x + 16
x² - 10 x - x = 16 - 25 + 9
x² - 11 x = 0
x = 0
( x - 2 ) ( x - 10 )
x - ∞ 2 10 + ∞
x - 2 - 0 + +
x - 10 - - 0 +
produit + 0 - 0 +
allez termine
