^2 means to the power of two

The domain is all x. There are no constraints on the domain. The range, however, is constrained, because the equation is a parabola (inverted) and has a vertex (maximum).

If you were thinking of plotting the graph then a “reasonable” domain would be one that can be drawn on, say, A4 paper which has a width of 21cm, about 8¼ inches. If we forget about the large constant we have y=-8.6x²+560x. When y=0, x=0 and 560/8.6=65 approx. So the vertex is about 32.5. The scale of the graph for the domain x should accommodate the width of a little more than 65. For demonstration purposes we can use a width of 80. That is a reasonable width, so the graph could go from x=-10 to +70 and would show the vertex and two points intersecting the line y=24000, the starting point for the y axis. The scale of the y axis needs to take into account the values for y when x=-10 and 70, bearing in mind that the vertex is around x=32.5 or thereabouts, when y is at its maximum value around 33000.

by Top Rated User (762k points)