Question

Determine as coordenadas do vértice:
Questão completa na imagem acima.​

Answer 1

Explicação passo-a-passo:

a) $\sf f(x)=-x^2+6x-10$

• $\sf x_V=\dfrac{-b}{2a}$

$\sf x_V=\dfrac{-6}{2\cdot(-1)}$

$\sf x_V=\dfrac{-6}{-2}$

$\sf x_V=3$

• $\sf y_V=\dfrac{-\Delta}{4a}$

$\sf \Delta=6^2-4\cdot(-1)\cdot(-10)$

$\sf \Delta=36-40$

$\sf \Delta=-4$

$\sf y_V=\dfrac{-(-4)}{4\cdot(-1)}$

$\sf y_V=\dfrac{4}{-4}$

$\sf y_V=-1$

Logo, $\sf V(3,-1)$

b) $\sf f(x)=x^2+2x$

• $\sf x_V=\dfrac{-b}{2a}$

$\sf x_V=\dfrac{-2}{2\cdot1}$

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

$\sf x_V=-1$

• $\sf y_V=\dfrac{-\Delta}{4a}$

$\sf \Delta=2^2-4\cdot1\cdot0$

$\sf \Delta=4-0$

$\sf \Delta=4$

$\sf y_V=\dfrac{-4}{4\cdot1}$

$\sf y_V=\dfrac{-4}{4}$

$\sf y_V=-1$

Logo, $\sf V(-1,-1)$