Question

Para a função f.(x)=x²-2x-8, determine:
b) o valor de x' e x"
c) o valor de x' e x"
d)o valor de x'+x"\x'.x"
f) o verticie

Answer 1

Olá Elizeu.


B & C - 

Encontrando as raízes da equação pelo método de completar quadrados:

$\mathsf{x^2-2x-8=0~+(1^2)}\\\\\mathsf{x^2-2x+1=8+1}\\\\\mathsf{(x-1)^2=9}\\\\\mathsf{\sqrt{(x-1)}^2=\pm\sqrt{9}}\\\\\mathsf{x-1=\pm3}\\\\\mathsf{x'=3+1}\\\\\boxed{\mathsf{x'=4}}\\\\\\\mathsf{x''=-3+1}\\\\\boxed{\mathsf{x''=-2}}$


D - 

$\mathsf{\dfrac{x'+x''}{x'\cdot x''}\Rightarrow \dfrac{4-2}{4\cdot(-2)}\Rightarrow \dfrac{2}{-8}\Rightarrow \boxed{\mathsf{-\dfrac{1}{4}}}}$


F - 

$\mathsf{xv=\dfrac{-b}{2a}\qquad\qquad\qquad\qquad\qquad yv=\dfrac{-\Delta}{4a}}\\\\\\\mathsf{xv=\dfrac{-(-2)}{2\cdot1}\qquad\qquad\qquad\qquad~ yv=\dfrac{-[(-2)^2-4\cdot1\cdot(-8)]}{4\cdot1}}\\\\\\\mathsf{xv=\dfrac{2}{2}\qquad\qquad\qquad\qquad\qquad~~ yv=\dfrac{-[4+32]}{4}}\\\\\\\mathsf{xv=1\qquad\qquad\qquad\qquad\qquad ~~~yv=\dfrac{-36}{4}}\\\\\\\boxed{\mathsf{xv=1}}\qquad\qquad\qquad\qquad\qquad\boxed{\mathsf{yv=-9}}$



Dúvidas? comente.