Answer: The correct option is (A). \(g(x)=(x+12)^2.\)
Step-by-step explanation: Given that the equation of the quadratic parent function is
\(f(x)=x^2~~~~~~~~~~~~~~~~~~~~~~~~``(i)\)
We are to find the equation of the new function after shifting the parent function (i) 12 units left.
Since we are shifting 12 units left, so there is a horizontal translation in the X-axis.
And the x co-ordinate becomes (x+12).
Therefore, the equation of the new function will be
\(g(x)=(x+12)^2.\)
Thus, the required equation of the new function is \(g(x)=(x+12)^2.\)
Option (A) is correct.
