Question

Dadas as funções, determine as coordenadas do vértice de cada uma delas. a) y = x2 - 4x - 5 b) y = –5x2 +8x -3 ​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{y = x^2 - 4x - 5}$

$\mathsf{\Delta = b^2 - 4.a.c}$

$\mathsf{\Delta = (-4)^2 - 4.1.(-5)}$

$\mathsf{\Delta = 16 + 20}$

$\mathsf{\Delta = 36}$

$\mathsf{y_V = -\dfrac{\Delta}{4a} = -\dfrac{36}{4}}$

$\boxed{\boxed{\mathsf{y_V = -9}}}$

$\mathsf{x_V = -\dfrac{b}{2a} = \dfrac{-4}{-2}}$

$\boxed{\boxed{\mathsf{x_V = 2}}}$

$\mathsf{y = -5x^2 + 8x - 3}$

$\mathsf{\Delta = b^2 - 4.a.c}$

$\mathsf{\Delta = (8)^2 - 4.(-5).(-3)}$

$\mathsf{\Delta = 64 - 60}$

$\mathsf{\Delta = 4}$

$\mathsf{y_V = -\dfrac{\Delta}{4a} = \dfrac{-4}{-20}}$

$\boxed{\boxed{\mathsf{y_V = \dfrac{1}{5}}}}$

$\mathsf{x_V = -\dfrac{b}{2a} = \dfrac{-8}{-10}}$

$\boxed{\boxed{\mathsf{x_V = \dfrac{4}{5}}}}$