Răspuns:
Forma canonică
[tex]\boldsymbol {\red{f(x) = a\bigg(x + \dfrac{b}{2a}\bigg)^2 + \dfrac{-\Delta}{4a}}}[/tex]
unde a, b, c sunt coeficienții reali, a≠0
f(x) = 2x² - 4x + 7
Coeficienții
a = 2, b = -4, c = 7
Discriminantul
[tex]\Delta = b^2 - 4ac = (-4)^2 - 4\cdot 2\cdot 7 = 16 - 56 = -40[/tex]
[tex]\dfrac{b}{2a} = \dfrac{-4}{2\cdot2} = - 1[/tex]
[tex]\dfrac{-\Delta}{4a} = \dfrac{-(-40)}{8} = \dfrac{40}{8} = 5[/tex]
Forma canonică:
[tex]\boldsymbol {\red{f(x) = 2(x - 1)^2 + 5}}[/tex]
g(x) = -x² - 10x - 11
a = -1, b = -10, c = -11
[tex]\Delta = (-10)^2 - 4\cdot(-1)\cdot(-11) = 100 - 44 = 56 \\ [/tex]
[tex]\dfrac{b}{2a} = \dfrac{ - 10}{2(-1)} = 5[/tex]
[tex]\dfrac{-\Delta}{4a} = \dfrac{-56}{4(-1)} = \dfrac{56}{4} = 14[/tex]
Forma canonică
[tex]\boldsymbol {\red{g(x) = -1(x + 5)^2 + 14}}[/tex]
