Răspuns:
Explicație pas cu pas:
[tex]\it f(x) = ax^2+bx+c \ \ \ (forma\ \ general\breve{a}) \\\;\\ Aici\ \ avem:\ f(x) = -x^2+4x+5 \Rightarrow a = -1\ \textless \ 0 \Rightarrow \\\;\\ \Rightarrow f(x) \ admite \ un\ maxim\ V\left(-\dfrac{b}{2a},\ -\dfrac{\Delta}{4a}\right)[/tex]
[tex]\it -\dfrac{b}{2a} = -\dfrac{4}{2\cdot{(-1)}} = 2 \\\;\\ \\\;\\ -\dfrac{\Delta}{4a}= -\dfrac{b^2-4ac}{4a} = -\dfrac{16-4\cdot{(-1)}\cdot5}{4\cdot{(-1)}} = \dfrac{16+20}{4} = \dfrac{36}{4}=9[/tex]
