2022 TMJC Promo Q6

A curve \(C\) undergoes, in succession, the following transformations.

\(A\): Translation of \(4\) units in the negative \(y\)- direction.

\(B\): Stretching parallel to the \(x\)-axis by a factor of \(2\).

\(C\): Reflection in the \(x\)-axis.

The equation of the resulting curve is \(y=\frac{{{x}^{2}}}{4}+4\).

Determine the equation of the original curve \(C\) before the transformations were carried out.[3]