Question

Va rog!!!
Dau coroana!!

Answer 1

Răspuns:

Explicație pas cu pas:

1) f(x) = 1/2(x^2 +4x +4) -5/4 = x^2/2 +2x +3/4

Cum coef. lui x^2 este 1/2 > 0 , f admite un minim

Varful V(-b/2a, -Δ/4a)

-b/2a = -2/1 = -2

-Δ/4a) = -1/(4*1/2)(4 - 4*1/2 * 3/4) =

 -1/2(4-3/2) = -1/2(5/2 = -5/4

V(-2, -5/4)

2) Gf ∩ Oy :

x = 0,  y = 1/3,  A(0, 1/3)

Gf ∩ Ox:

y = 0,      1/6(12x^2 -11x +2) = 0

12x^2 -11x +2 = 0

delta = 121 - 96 = 25

x1,2 = (11 +- 5)/24

x1 = 6/14 = 1/4

x2 = 16/24 = 4/6 = 2/3

B(1/4, 0)  , C(2/3, 0)