What will be the equation of translated parabola if the parabola $y^{2} = 4 x$ is translated to $(0, - 2)$ ?

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Solution

Given equation of parabola as: $y^{2} = 4 x$
Now, the parabola is translated vertically to a point $(0, - 2) .$
Now, as we know that the general equation of vertically translated parabola is $(y - k)^{2} = 4 a x$
Where $k$ is y-coordinate to which the parabola is shifted.
Thus, On comparing we get the equation of translated parabola as: $(y + 2)^{2} = 4 x$ $[∵ k = - 2, a = 1]$

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