Graphing Quadratic Inequalities

To graph the quadratic inequality, we will follow three steps.

1. Graph the related quadratic function.
2. Test a point not on the parabola.
3. Shade accordingly. If the point satisfies the inequality, we shade the region that contains the point. If not, we shade the opposite region.

Step $1$

Let's draw the graph of the related function, $W=115x^2.$ Since $x$ represents the diameter of the suspender cables, we will draw it for non-negative values of $x.$

Step $2$

Next, let's determine which region to shade by testing a point. We will use $(2,100)$ as our test point. Let's see if it satisfies the given inequality.

Step $3$

Since $(2,100)$ produced a true statement, we will shade the region that contains the point. Also, note that the inequality is not strict. Therefore, the parabola will be solid.

The shaded region represents weights that can be safely supported by a suspension bridge with cables with various diameter.