Question

determine as cordenadas do vértice da função
f(x)=2x²-3x+2
f(x)=x²-8x-16

Answer 1

Olá Talyson,
tudo bem?
Vamos lá:

$f(x)=2x^2-3x+2\\ \\ 2x^2-3x+2=0\\ \\ \Delta=b^2-4ac\\ \\ \Delta=(-3)^2-4\cdot{2}\cdot{2}\\ \\ \Delta=9-16\\ \\ \Delta=-7\\ \\ \text{cordenadas do v\'{e}rtice:}\\ \\ x_{v}=\frac{-b}{2a}\ y_{v}=\frac{-\Delta}{4a}\\ \\ \text{substitui:}\\ \\ x_{v}=\frac{-(-3)}{2\cdot{2}}\to \boxed{x_{v}=\frac{3}{4}}\ y_{v}=\frac{-(-7)}{4\cdot{2}}\to \boxed{y_{v}=\frac{7}{8}}$
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$f(x)=x^2-8x-16\\ \\ \Delta=(-8)^2-4\cdot{1}\cdot{(-16)}\\ \\ \Delta=64+64\\ \\ \Delta=128\\ \\ x_{v}=\frac{-(-8)}{2\cdot{1}}\to x_{v}=\frac{8}{2}\to \boxed{x_{v}=4}\ y_{v}=\frac{-128}{4\cdot{1}}\to \boxed{y_{v}=-32}$

Espero ter ajudado.