Question

Considere a parabola determinada pela função quadratica f(x) = x 2 + 4x − 5. Determine as coordenadas do vertice da parabola.

Answer 1

$x {}^{2} + 4x + - 5 = 0 \\ d = 4 {}^{2} - 4.1.( - 5) \\ d = 16 - 4( - 5) \: \: \: \: \: \\ d = 16 + 20 \: \: \: \: \: \: \: \: \: \: \: \: \\ d = 36 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ x = \frac{ - 4 + - \sqrt{36} }{2} \\ \\ x = \frac{ - 4 + - 6}{2} \: \: \: \: \: \: \: \: \\ \\ x1 = \frac{ - 4 + 6}{2} = \frac{2}{2} = 1 \\ \\ x2 = \frac{ - 4 - 6}{2} = \frac{ - 10}{2} = - 5$

$xv = - \frac{4}{2} = 2 \\ \\yv = - \frac{36}{4.2} = \frac{36}{8} = 4.5$