Question

determine a função quadrática representada na figura​

Answer 1

Resposta final:
Y= - 2x2 +3x+2

Desenvolvimento na foto.

Answer 2

$A(-\dfrac{1}{2}, 0)\\B(2,0)\\C(0,2)$

$f(0)=a.{0}^{2}+b.0+c\\c=2$

$f(2)=a{2}^{2}+b.2+c\\4a+2b+2=0\\4a+2b=-2\div(2)\\2a+b=-1$

$f(-\dfrac{1}{2})=a.{(-\dfrac{1}{2})}^{2}+b(-\dfrac{1}{2})+2\\\dfrac{a}{4}-\dfrac{b}{2}+2=0\times(4)$

$a-2b+8=0\\a-2b=-8$

$\begin{cases}2a+b=-1\\a-2b=-8\end{cases}$

multiplicando a primeira equação por 2 temos

$+\begin{cases}4a+2b=-2\\a-2b=-8\end{cases}$

$5a=-10\\a=-\dfrac{10}{5}\\a=-2$

$2a+b=-1\\2(-2)+b=-1\\-4+b=-1\\b=4-1=3$

$\boxed{\boxed{\bf{f(x)=-2{x}^{2}+3x+2}}}$