Quadratic Equation Discriminant

Samantha is analyzing a quadratic equation given by the expression:

$$f(x) = 2x^2 - 4x + k$$

where $$k$$ is a constant that can vary. Her goal is to determine the values of $$k$$ for which the equation has exactly one solution. A quadratic equation has exactly one solution when its discriminant is zero. The discriminant $$D$$ of a quadratic equation $$ax^2 + bx + c$$ is calculated using the formula:

$$D = b^2 - 4ac$$

Using this information, what is the value of $$k$$ that results in exactly one solution for the equation $$f(x) = 0$$?