Question

If the parabola $(y+1{)}^2=8x-4$ is translated 2 units along positive y-axis and 3 units along negative x-axis, then find the coordinates of the new vertex?

Answer 1

Given the equation of parabola $(y+1{)}^2=8x-4$
on re-arranging it into standard equation we get,
$\Rightarrow (y+1{)}^2=8(x-\frac{1}{2})$
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:

$(y+1-2{)}^2=8(x-\frac{1}{2}-(-3\left)\right)$
$\Rightarrow (y-1{)}^2=8(x+\frac{5}{2})$
Thus, the equation of translated parabola is
$(y-1{)}^2=8(x+\frac{5}{2})$
Hence, the new vertex of translated parabola is given by $(-\frac{5}{2},1).$