Question

Se x e y são as coordenadas do vértice da parábola y = 3x² - 5x + 9, então x + y é igual a: a) 5/6 b) 31/14 c) 83/12 d) 89/12 e) 89/18 f) 93/12

Answer 1

Explicação passo-a-passo:

$y=3x^2-5x+9$

$\bullet~x_V=\dfrac{-b}{2a}$

$x_V=\dfrac{-(-5)}{2\cdot3}$

$x_V=\dfrac{5}{6}$

$\bullet~y_V=\dfrac{-\Delta}{4a}$

$\Delta=(-5)^2-4\cdot3\cdot9$

$\Delta=25-108$

$\Delta=-83$

$y_V=\dfrac{-(-83)}{4\cdot3}$

$y_V=\dfrac{83}{12}$

Assim:

$x+y=\dfrac{5}{6}+\dfrac{83}{12}$

$x+y=\dfrac{10}{12}+\dfrac{83}{12}$

$x+y=\dfrac{93}{12}$