Question

Determine as coordenadas do vértice da parábola das funções quadráticas a

seguir.

f(x) = –4x²+ 4x + 5​

Answer 1

Explicação passo-a-passo:

• Vértice

• $\sf x_V=\dfrac{-b}{2a}$

$\sf x_V=\dfrac{-4}{2\cdot(-4)}$

$\sf x_V=\dfrac{-4}{-8}$

$\sf x_V=\dfrac{1}{2}$

• $\sf y_V=\dfrac{-\Delta}{4a}$

$\sf \Delta=4^2-4\cdot(-4)\cdot5$

$\sf \Delta=16+80$

$\sf \Delta=96$

$\sf y_V=\dfrac{-96}{4\cdot(-4)}$

$\sf y_V=\dfrac{-96}{-16}$

$\sf y_V=6$

O vértice é $\sf V\left(\dfrac{1}{2},6\right)$

• Raízes

$\sf -4x^2+4x+5=0$

$\sf \Delta=4^2-4\cdot(-4)\cdot5$

$\sf \Delta=16+80$

$\sf \Delta=96$

$\sf x=\dfrac{-4\pm\sqrt{96}}{2\cdot(-4)}=\dfrac{-4\pm4\sqrt{6}}{-8}$

$\sf x'=\dfrac{-4+4\sqrt{6}}{-8}~\rightarrow~x'=\dfrac{1-\sqrt{6}}{2}$

$\sf x"=\dfrac{-4-4\sqrt{6}}{-8}~\rightarrow~x"=\dfrac{1+\sqrt{6}}{2}$