Question

Fie functia h:R-R,h(x)=x(puterea a 2)+4x-5 realizati graficul

Answer 1

x=0=>f(0)=0+0-5=-5=>C(0;-5)=Gf∩Oy

f(x)=0

x²+4x-5=0

Δ=4²-4*1*(-5)=16+20=36

Δ>0=>Gf∩Ox in doua puncte A(x₁;0) si B(x₂;0)

x₁=(-4-6)/2=-10/2=-5=>A(-5;0)

x₂=(-4+6)/2=2/2=1=>B(1;0)

a>0=>functia are un minim

V(xv;yv)

xv=-4/2=-2=>punctul de simetrie

yv=f(xv)=4-8-5=-9

V(-2;-9) (minim)

x    | -∞    -9   -5  -2   0  1  +∞

h(x)|↓↓↓↓0↓↓0↓-9↑-5↑0↑↑