Question

determine o vértice da parábola da função y=2x²+8 x-6

Answer 1

$y= 2x^2 + 8x - 6 \\ \\ a = 2 \\ b =8 \\ c = -6$

Abscissa do vértice:

$X_V = \frac{-b}{2a} \\ \\ X_V = \frac{-8}{2\cdot2} \\ \\ X_V = \frac{-8}{4} \\ \\ \boxed{X_V = -2}$

Ordenada do vértice:

$Y_V = \frac{-\Delta}{4a} \\ \\ Y_V = \frac{-(b^2-4ac)}{4a} \\ \\ Y_V = \frac{-(8^2-4\cdot2\cdot(-6))}{4\cdot2} \\ \\ Y_V = \frac{-112}{8} \\ \\ \boxed{Y_V = -14}$

Coordenadas do vértice:

$V = (X_V;\,Y_V) \\ \\ \boxed{\boxed{V = (-2;\,-14)}}$