How do you graph the inequality x^2 + 7x + 6 <=6x2+7x+6≤6?

2 Answers
Nghi N.
Mar 22, 2016

Graph quadratic function.

Explanation:

y = x^2 + 7x + 6 <= 6 y=x2+7x+6≤6
y = x^2 + 7x <= 0y=x2+7x≤0
y = x(x + 7) < = 0y=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) = -7/2x=−b2a=−72
y-coordinate of vertex:
y(-7/2) = (-7/2)(7/2) = -49/4y(−72)=(−72)(72)=−494
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.

Helen D.
Mar 22, 2016

I would use desmos web graphing calculator to graph
y<=x^2+7xy≤x2+7x to obtain plot

enter image source here

desmos.com

Related questions
See all questions in Linear Inequalities in Two Variables
Impact of this question
3285 views around the world
You can reuse this answer
Creative Commons License