Question

y=2x elevado a 2-3x-2
coordenadas do vértice

Answer 1

O vértice é o ponto $V(x_{V}, y_{V})$, onde

$x_{V}=-\dfrac{b}{2a}\\ \\ y_{V}=-\dfrac{\Delta}{4a}=\dfrac{4ac-b^{2}}{4a}$


$y=2x^{2}-3x-2\\ \\ \\ a=2\\ \\ b=-3\\ \\ c=-2\\ \\ \\ x_{V}=-\dfrac{\left(-3 \right )}{2\cdot \left(2 \right )}\\ \\ x_{V}=\dfrac{3}{4}\\ \\ \\ y_{V}=\dfrac{4\cdot\left(2\right)\cdot \left(-2 \right )-\left(-3 \right )^{2}}{4 \cdot \left(2 \right )}\\ \\ y_{V}=\dfrac{-16-9}{8}\\ \\ y_{V}=-\dfrac{25}{8}$


O vétice é o ponto $V\left(\dfrac{3}{4},\,-\dfrac{25}{8}\right)$.