Final answer:
The parabola described by the equation y=2x² opens upwards and has its vertex at the origin, indicating that y is never less than zero. Thus, there are no values of x for which y is less than zero.
Step-by-step explanation:
The question asks to find the range of values for which y is less than zero given the equation y=2x². To find this range, we need to analyze the properties of the parabolic function represented by the equation. In general, the graph of a parabola opens upwards when the coefficient of x² is positive and opens downwards when it is negative.
Since the coefficient of x² in the equation is positive (2), the parabola opens upwards. The vertex of the parabola, which is the highest or lowest point, represents the minimum or maximum value of y. In this case, the vertex is at the origin (0,0) since there is no constant or linear term, indicating that the parabola has a minimum at y = 0. Hence, for all values of x, y will always be greater than or equal to zero, so there are no values of x for which y is less than zero. Therefore, the range of values for which y is less than zero is empty.