Question

Encontre as raizes e as coordenadas do vertice


F(x)= x² + 4x +1

Answer 1

Resposta:

$\text{Leia abaixo}$

Explicação passo-a-passo:

$\sf f(x) = x^2 + 4x + 1$

$\sf \Delta = b^2 - 4.a.c$

$\sf \Delta = 4^2 - 4.1.1$

$\sf \Delta = 16 - 4$

$\sf \Delta = 12$

$\sf x = \dfrac{-b \pm \sqrt{\Delta}}{2a}$

$\sf x' = \dfrac{-4 + \sqrt{12}}{2.1} = \dfrac{-4 + 2\sqrt{3}}{2} = -2 + \sqrt{3}$

$\sf x'' = \dfrac{-4 - \sqrt{12}}{2.1} = \dfrac{-4 - 2\sqrt{3}}{2} = -2 - \sqrt{3}$

$\boxed{\boxed{\sf \text{S} = \text{\{}-2 + \sqrt{3}, -2 - \sqrt{3}{\}}}}$

$\sf \text{V}_x = -\dfrac{b}{2a} = -\dfrac{4}{2} = -2$

$\sf \text{V}_y = -\dfrac{\Delta}{4a} = -\dfrac{12}{4} = -3$

$\boxed{\boxed{\sf \text{V(-2,-3)}}}$