Question

solve for ( x ) and graph the solution.
( -4(x + 1)(x + 2) geq 0 )
plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.
submit

Explanation:

Step1: Find the roots

Set \(-4(x + 1)(x + 2)=0\). Then \(x+1 = 0\) gives \(x=-1\), and \(x + 2=0\) gives \(x=-2\).

Step2: Analyze the sign of the quadratic function

The quadratic function \(y=-4(x + 1)(x + 2)=-4(x^{2}+3x + 2)=-4x^{2}-12x-8\), the coefficient of \(x^{2}\) is \(-4<0\), the parabola opens downwards.

Step3: Determine the solution of the inequality

We want to find when \(-4(x + 1)(x + 2)\geq0\). The parabola \(y =-4(x + 1)(x + 2)\) is non - negative (above or on the \(x\) - axis) for \(x\in[-2,-1]\)

Answer:

The solution of the inequality \(-4(x + 1)(x + 2)\geq0\) is \(x\in[-2,-1]\). On the number - line, we plot closed circles at \(x=-2\) and \(x =-1\) and shade the segment between them.