To graph the quadratic function y=-2x^2 using the given values of x, one can create a table with two columns: one for x and the other for y. Starting with x=-2, we can substitute this value into the equation to find the corresponding value of y, which is y=-8. Similarly, by substituting -1, 0, 1, and 2 into the equation, we can find corresponding values of y as 2, 0, -2, and -8, respectively. By plotting these points on a graph and connecting them, we get a downward facing parabola with its vertex at (0,0).