Question

O VÉRTICE da parábola y = 2x2

- 4x + 6 é o ponto:

A) (2,5)
B) (3,4)
C) (-4,6)
D) (1,4)

Answer 1

Olá!

y = 2x² - 4x + 6

a = 2

b = -4

c = 6

O ponto do vértice da função é dado por:

$x_{v} =\dfrac{-b}{2a} ~~~~~e~~~~~y_{v}=-\dfrac{\Delta}{4a}$

Então:

$x_{v} =\dfrac{-b}{2a}~~~~~\to ~~~~-\dfrac{(-4)}{2\cdot2}~~~~~\to ~~~~\dfrac{4}{4}~~~~~\to ~~~~~\boxed{x_{v}=1 }$

$y_{v}=-\dfrac{\Delta}{4a}~~~~~\to ~~~~~\dfrac{-[(-4)^{2}-4\cdot 2\cdot 6]}{4\cdot 2}~~~~~\to ~~~~~\dfrac{32}{8}~~~~~\to ~~~~~\boxed{y_{v}=4}$

Resposta:

Vértice:

$(x_{v},y_{v} )=(1,4)$

Letra D)

:)