Question

determine as coordenadas (x,y) do vértice da parábola que representa a função:
y=x²+6x+11​

Answer 1

$\sf{\Rightarrow y=x^{2}+6x+11}$

• $\sf{a=1}$

• $\sf{b=6}$

• $\sf{c=11}$

$\sf{\Rightarrow∆=b²-4.a.c}$

• $\sf{\Delta=(6)^{2}-4.(1).(11)}$

• $\sf{\Delta=36-44}$

• $\sf{\Delta=-8}$

$\sf{\Rightarrow xv=-b/2a}$

• $\sf{xv=-\dfrac{(6)}{2.(1)}}$

• $\sf{xv=-\dfrac{6}{2}}$

• $\sf{xv=-3}$

$\sf{\Rightarrow yv=-\dfrac{∆}{4a}}$

• $\sf{yv=-\dfrac{(-8)}{4.(1)}}$

• $\sf{yv=\dfrac{8}{4}}$

• $\sf{yv=2}$

▶️As coordenadas será: { -3 , 2 }

Answer 2

xv = -b/2a = -6/2.1= -6/2 = -3.

yv =f(-3)= (-3)² +6.(-3) +11= 9-18+11=20-18= 2

V( -3, 2)