Question

How do you solve `3x^2+24x>=-41` by graphing?

Answer 1

x-axis with the gap `(-4-sqrt(7/3), -4+sqrt(7/3))`. See this gap in the graph.

Explanation:

`x^2+24x=3(x+4)^2-48>=-41 to x >=-4+sqrt(7/3) and x<=-4-sqrt(7/3)`

The 2-D graph is for {(x, y)}, satisfying `3x^2+24x>=-41`.

The x-axis sans the gap

`(-4-sqrt(7/3), -4+sqrt(7/3))=(-5.5275, -2.4725)` is 1-D solution ,

In 3-D, the gap is cylindrical, about the x-axis..

graph{3x^2+24x+41>=0 [-10, 10, -5, 5]}