The correct option is C (−52,1)
Given the equation of parabola (y+1)2=8x−4
on re-arranging it into standard equation we get,
⇒(y+1)2=8(x−12)
Now, according to question this parabola is translated 2 units along the positive y-axis and 3 units along negative x-axis.
Thus, we get the translated equation of the parabola as:
(y+1−2)2=8(x−12−(−3))
⇒(y−1)2=8(x+52)
Thus, the equation of translated parabola is
(y−1)2=8(x+52)
Hence, the new vertex of translated parabola is given by (−52,1).