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

Mar 22, 2016

#### Explanation:

$y = {x}^{2} + 7 x + 6 \le 6$
$y = {x}^{2} + 7 x \le 0$
$y = x \left(x + 7\right) < = 0$ (1)
First, graph the parabola y = x(x + 7) = 0 by the vertex and the 2 x-intercepts.
x-coordinate of vertex:
$x = - \frac{b}{2 a} = - \frac{7}{2}$
y-coordinate of vertex:
$y \left(- \frac{7}{2}\right) = \left(- \frac{7}{2}\right) \left(\frac{7}{2}\right) = - \frac{49}{4}$
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.

Mar 22, 2016

I would use desmos web graphing calculator to graph
$y \le {x}^{2} + 7 x$ to obtain plot

desmos.com