Question

How do you graph the inequality `x^2 + 7x + 6 <=6`?

Answer 1

Graph quadratic function.

Explanation:

`y = x^2 + 7x + 6 <= 6`
`y = x^2 + 7x <= 0`
`y = x(x + 7) < = 0` (1)
First, graph the parabola y = x(x + 7) = 0 by the vertex and the 2 x-intercepts.
x-coordinate of vertex:
`x = -b/(2a) = -7/2`
y-coordinate of vertex:
`y(-7/2) = (-7/2)(7/2) = -49/4`
The 2 x-intercepts are --> y = 0 --> x = 0 and x = -7.
The solution set of the inequality (1) is the area below the parabola.
graph{x(x + 7) [-40, 40, -20, 20]}
Note. The parabola is included in the solution set.

Answer 2

I would use desmos web graphing calculator to graph
`y<=x^2+7x` to obtain plot

desmos.com