Question

Para cada uma das funções abaixo obtenha o vértice da parábola:
A) F(x) = x^2-10x+21
B)G(x) = x^2-2x
C) H(x) = x^2-1
D) M(x) = x^2+14x+49

Answer 1

Explicação passo-a-passo:

a) $\sf f(x)=x^2-10x+21$

• $\sf x_V=\dfrac{-b}{2a}$

$\sf x_V=\dfrac{-(-10)}{2\cdot1}$

$\sf x_V=\dfrac{10}{2}$

$\sf x_V=5$

• $\sf y_V=\dfrac{-\Delta}{4a}$

$\sf \Delta=(-10)^2-4\cdot1\cdot21$

$\sf \Delta=100-84$

$\sf \Delta=16$

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

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

$\sf y_V=-4$

O vértice é $\sf V(5,-4)$

b) $\sf g(x)=x^2-2x$

• $\sf x_V=\dfrac{-b}{2a}$

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

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

$\sf x_V=1$

• $\sf y_V=\dfrac{-\Delta}{4a}$

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

$\sf \Delta=4-0$

$\sf \Delta=4$

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

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

$\sf y_V=-1$

O vértice é $\sf V(1,-1)$

c) $\sf h(x)=x^2-1$

• $\sf x_V=\dfrac{-b}{2a}$

$\sf x_V=\dfrac{-0}{2\cdot1}$

$\sf x_V=\dfrac{-0}{2}$

$\sf x_V=0$

• $\sf y_V=\dfrac{-\Delta}{4a}$

$\sf \Delta=0^2-4\cdot1\cdot(-1)$

$\sf \Delta=0+4$

$\sf \Delta=4$

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

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

$\sf y_V=-1$

O vértice é $\sf V(0,-1)$

d) $\sf m(x)=x^2+14x+49$

• $\sf x_V=\dfrac{-b}{2a}$

$\sf x_V=\dfrac{-14}{2\cdot1}$

$\sf x_V=\dfrac{-14}{2}$

$\sf x_V=-7$

• $\sf y_V=\dfrac{-\Delta}{4a}$

$\sf \Delta=14^2-4\cdot1\cdot49$

$\sf \Delta=196-196$

$\sf \Delta=0$

$\sf y_V=\dfrac{-0}{4\cdot1}$

$\sf y_V=\dfrac{-0}{4}$

$\sf y_V=0$

O vértice é $\sf V(-7,0)$