Question

Dada a função y = -x² + 4x – 3, determine as coordenadas do vértice:
O x = -2; y = 1
x = -2; y = -1
x = 2; y = 1
x = 4; y = - 3
0 x = 2: y = -1

Answer 1

Explicação passo-a-passo:

$\sf y = - x^2 + 4x - 3$

coeficientes: a = -1, b = 4, c = -3

Vértice do x:

$\sf x_v = \dfrac{- b}{2a} = \dfrac{- (4)}{2*(-1)} = \dfrac{- 4}{-2} = \red{2}$

Vértice do y

$\sf \Delta = b^2 - 4ac$

$\sf \Delta = (4)^2 - 4*(-1)*(-3)$

$\sf \Delta = 16 - 12$

$\sf \Delta = 4$

$\sf y_v = \dfrac{- \Delta}{4a} = \dfrac{- (4)}{4*(-1)} = \dfrac{-4}{-4} = \red{ 1}$

V(xv , yv) >>> V(2 , 1)