The gradient of a curve at a point is the slope of the tangent line to the curve at that point. To find the point \((x, y)\) on the curve \(y = 2x^2 - 2x + 3\) where the gradient is \(2\), we need to find the derivative of the curve and then solve for the \(x\) value where the derivative is \(2\).

Given the equation \(y = 2x^2 - 2x + 3\), take the derivative with respect to \(x\) to find the gradient function:

\(\frac{dy}{dx} = \frac{d}{dx} (2x^2 - 2x + 3) = 4x - 2\)

Now, set the derivative equal to \(2\) and solve for \(x\):

\(4x - 2 = 2\)

\(4x = 4\)

\(x = 1\)

Now that we have the \(x\) value, substitute it into the original equation to find the corresponding \(y\) value:

\(y = 2x^2 - 2x + 3 = 2(1)^2 - 2(1) + 3 = 2 - 2 + 3 = 3\)

So, the point on the curve where the gradient is \(2\) is \((1, 3)\),