Question

obtém as vértices de cada uma das parábolas representativas das funções quadráticas

a) y = x² - 6x + 4

b) y = -2x² - x + 3

c) y = x² - 9​

Answer 1

a) y = x² - 6x + 4

$\frac{d}{dx}\left(x^2-6x+4\right)\\\\=\frac{d}{dx}\left(x^2\right)-\frac{d}{dx}\left(6x\right)+\frac{d}{dx}\left(4\right)\\\\Resolvendo, chegamos.. a\\=2x-6+0\\\\\mathrm{Simplificando}\\\\=2x-6$

b) y = -2x² - x + 3

$\frac{d}{dx}\left(-2x^2-x+3\right)\\\\=-\frac{d}{dx}\left(2x^2\right)-\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(3\right)\\\\Novamente\\\\=-4x-1+0\\\\=-4x-1$

c) y = x² - 9​

$\frac{d}{dx}\left(x^2-9\right)\\\\=\frac{d}{dx}\left(x^2\right)-\frac{d}{dx}\left(9\right)\\\\Resolvemos.. e\\\\=2x-0\\\\=2x$