Question

Calcule o x do vértice e o y do vértice das funções relacionadas abaixo: a) y = x² - x - 6 b) y = 2x² + 3x - 2 c) y = x² + 3x - 4 d) y = x² - 4x

Answer 1

Explicação passo-a-passo:

a) $\sf y=x^2-x-6$

• $\sf x_V=\dfrac{-b}{2a}$

$\sf x_V=\dfrac{-(-1)}{2\cdot1}$

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

• $\sf y_V=\dfrac{-\Delta}{4a}$

$\sf \Delta=(-1)^2-4\cdot1\cdot(-6)$

$\sf \Delta=1+24$

$\sf \Delta=25$

$\sf y_V=\dfrac{-25}{4\cdot1}$

$\sf y_V=\dfrac{-25}{4}$

b)

$\sf y=2x^2+3x-2$

• $\sf x_V=\dfrac{-b}{2a}$

$\sf x_V=\dfrac{-3}{2\cdot2}$

$\sf x_V=\dfrac{-3}{4}$

• $\sf y_V=\dfrac{-\Delta}{4a}$

$\sf \Delta=3^2-4\cdot2\cdot(-2)$

$\sf \Delta=9+16$

$\sf \Delta=25$

$\sf y_V=\dfrac{-25}{4\cdot2}$

$\sf y_V=\dfrac{-25}{8}$

c)

$\sf y=x^2+3x-4$

• $\sf x_V=\dfrac{-b}{2a}$

$\sf x_V=\dfrac{-3}{2\cdot1}$

$\sf x_V=\dfrac{-3}{2}$

• $\sf y_V=\dfrac{-\Delta}{4a}$

$\sf \Delta=3^2-4\cdot1\cdot(-4)$

$\sf \Delta=9+16$

$\sf \Delta=25$

$\sf y_V=\dfrac{-25}{4\cdot1}$

$\sf y_V=\dfrac{-25}{4}$

d)

$\sf y=x^2-4x$

• $\sf x_V=\dfrac{-b}{2a}$

$\sf x_V=\dfrac{-(-4)}{2\cdot1}$

$\sf x_V=\dfrac{4}{2}$

$\sf x_V=2$

• $\sf y_V=\dfrac{-\Delta}{4a}$

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

$\sf \Delta=16-0$

$\sf \Delta=16$

$\sf y_V=\dfrac{-16}{4\cdot1}$

$\sf y_V=\dfrac{-16}{4}$

$\sf y_V=-4$