Question

Determinati a apartine lui R f(x)=-x^2+ax+b are maximul 4 in punctul x=-1

Answer 1

$f(x) = -x^2+ax+b\\ \\ Are maximul 4 in punctul x = -1. \\ \\ \Rightarrow V\Big(-\dfrac{b'}{2a'},-\dfrac{\Delta}{4a'}\Big) = V(-1,4) \\ \\ \Rightarrow \left\{ \begin{array}{ll} -\dfrac{b'}{2a'} = -1 \\ \\-\dfrac{\Delta}{4a'} = 4 \end{array} \right \Rightarrow \left\{ \begin{array}{ll} -\dfrac{a}{2\cdot (-1)} = -1 \\ \\-\dfrac{b'^2-4a'c'}{4a'} = 4 \end{array} \right \Rightarrow$

[tex]\Rightarrow \left\{ \begin{array}{ll} \dfrac{a}{-2} = 1 \\ -\dfrac{a^2-4\cdot (-1)\cdot b}{4\cdot (-1)} = 4 \end{array} \right \Rightarrow \left\{ \begin{array}{ll} a = -2 \\ -\dfrac{(-2)^2+4b}{-4} = 4 \end{array} \right \Rightarrow \\ \\ \Rightarrow \left\{ \begin{array}{ll} a = -2 \\ 4+4b = 16 \end{array} \right \Rightarrow \left\{ \begin{array}{ll} a = -2 \\ 4b = 12 \end{array} \right \Rightarrow \left\{ \begin{array}{ll} a = -2 \\ b = 3 \end{array} \right |[/tex]