Step 1 :The parent function in this case is \(y=x^{2}\).
Step 2 :A vertical compression by a factor of 2 would mean that the y-values of the function are halved.
Step 3 :This corresponds to multiplying the function by a factor of 1/2.
Step 4 :Therefore, the equation that compresses the parent function vertically by a factor of 2 should be \(y=\frac{1}{2} x^{2}\).
Step 5 :Final Answer: The equation that compresses the parent function vertically by a factor of 2 is \(\boxed{y=\frac{1}{2} x^{2}}\).