Question

Determinați coordonatele vârfului parabolei asociate funcției f:R->R f(x)=x la puterea 2+2x+4. // va rog sa-mi si explicati

Answer 1

$f:\mathbb_{R} \rightarrow \mathbb_{R}, \quad f(x) = x^2+2x+4 \\ \\ Coordonatele varfului parabolei asociate functiei: V\Big( \dfrac{-\Delta}{4a}, \dfrac{-b}{2a}\Big) \\ \\ a = 1;\quad b = 2;\quad c = 4; \\ \\ \Delta = b^2-4ac = 2^2 - 4\cdot 1\cdot 4 = 4-16 = -12 \\ \\ \Rightarrow V\Big( \dfrac{-\cdot(-12)}{4\cdot 1}, \dfrac{-2}{2\cdot 1}\Big) \Leftrightarrow V\Big( \dfrac{12}{4}, \dfrac{-2}{2}\Big) \Leftrightarrow \boxed{V\big(3, -1\big)}$