Question

A) Considere uma função de segundo grau tipo ax²+bx-c
Sendo a=1;b=2 e c=27

B) encontre as raízes da função, x do vértice e y do vértice.

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{f(x) = ax^2 + bx - c}$

$\mathsf{f(x) = x^2 + 2x - 27}$

$\mathsf{x^2 + 2x - 27 = 0}$

$\mathsf{\Delta = b^2 - 4.a.c}$

$\mathsf{\Delta = (2)^2 - 4.1.(-27)}$

$\mathsf{\Delta = 4 + 108}$

$\mathsf{\Delta = 112}$

$\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{-2 \pm \sqrt{112}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{-2 + 4\sqrt{7}}{2} = -1 + 2\sqrt{7}}\\\\\mathsf{x'' = \dfrac{-2 - 4\sqrt{7}}{2} = -1 - 2\sqrt{7}}\end{cases}}$

$\boxed{\boxed{\mathsf{S = \{1 + 2\sqrt{7};-1 -2\sqrt{7}\}}}}$

$\mathsf{x_V = -\dfrac{b}{2a} = -\dfrac{2}{2} = -1}$

$\mathsf{y_V = -\dfrac{\Delta}{4a} = -\dfrac{112}{4} = -28}$

$\boxed{\boxed{\mathsf{V(-1;-28)}}}$