Question

sa se determine functia f:R -R, f(x)=x^2+bx+c, stiind ca parabola care este reprezentarea grafica a functiei f are virful V(2;3).

Answer 1

V(-b/2a; -∆/4a)=V(2;3)
f(x)=x²+bx+c, a=1
(caci f(x) are forma f(x)=ax²+bx+c)

→-b/2a=2 ↔ -b/2=2 ↔b=-4
∆=b²-4ac=(-4)²-4c=16-4c=4(4-c)
→ -∆/4a=-4(4-c)/4=-(4-c)
-∆/4a=3
➡ -(4-c)=3
c-4=3
c=3+4
c=7

Deci f(x)=x²-4x+7