Question

Sa se scrie sub forma canonica funcția de gradul II:
f(x) = –3x2 – 8x + 11.

Answer 1

$\it f(x)=ax^2+bx+c\\ \\ Forma\ \ canonic\breve a\ a\ func\c{\it t}iei\ este:\\ \\ f(x)=a\Big(x+\dfrac{b}{2a}\Big)^2+\dfrac{-\Delta}{4a}$

Pentru funcția dată, avem:

$\it f(x)=-3x^2-8x+11,\ \ a=-3,\ \ b=-8,\ \ c=11\\ \\ \\ \dfrac{b}{2a}=\dfrac{-8}{-6}=\dfrac{\ 8^{(2}}{6}=\dfrac{4}{3}\\ \\ \\ \Delta = b^2-4ac=64+132=196\\ \\ \\ \dfrac{-\Delta}{4a}=\dfrac{-196}{-12}=\dfrac{\ 196^{(4}}{12}=\dfrac{49}{3}\\ \\ \\ f(x)=-3\Big(x+\dfrac{4}{3}\Big)^2+\dfrac{49}{3}$