Question

Qual o foco da Parábola y=x^2 - 4x + 5?

Answer 1

$\Delta = b^{2} -4ac$

16 -(4 * 5)

-4

$Yv = \frac{-\Delta}{4a}$

-(-4)/4

1

$Xv = \frac{-b}{2a}$

-(-4)/2

2

p = 1/4a

p = 1/4

(Xv , Yv + p)

1/4 + 1

(4 + 1)/4

5/4

{2 , 5/4}

Answer 2

y=x²-4x+5

y=x²-4x+4 +1

y=(x-2)²+1

(x-2)²=y-1 comparando com (x + xo )² = 2p.( y + yo )

Vértice = (2,1) ....2p=1 ==> p=1/2

Foco=(2 , 1+p/2) =(2,1+1/4)=(2,5/4)