Question

f (×)=2×la puterea2 -4×+5
sa se scrie sub forma canonica functia f: R-> R

Answer 1

Salut,

$Formula\ pentru\ forma\ canonic\breve{a}\ este:\ f(x)=a\left(x+\dfrac{b}{2a}\right)^2-\dfrac{\Delta}{4a}.\\\\a=2,\ b=-4,\ c=5.\\\\\Delta=b^2-4\cdot a\cdot c=(-4)^2-4\cdot 2\cdot 5=16-40=-24.\\\\f(x)=2x^2-4x+5=2\left(x-\dfrac{4}{4}\right)^2-\dfrac{-24}{8}=2(x-1)^2+3.\\\\Verificare:\ 2(x-1)^2+3=2(x^2-2x+1)+3=2x^2-4x+5,\\\\deci\ solu\c{t}ia\ este\ corect\breve{a}.$

Green eyes.