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

2 Answers
Mar 22, 2016

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.

Mar 22, 2016

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

enter image source here

desmos.com