Question

Select the graph that correctly displays the solution of:y < –x² – 4x.

Answer 1

Graph C

Explanation:

Given the inequality:

`y<-x^2-4x`

• The ,coefficient of x² is negative,, so the parabola ,opens downwards.

,

• This means either Option C or D is correct.

However, considering the critical points of the boundary line:

`\begin{gathered} y=-x^2-4x \\ -x(x+4)=0_{} \\ x=0\text{ or }x+4=0_{} \\ x=0\text{ or }x=-4 \end{gathered}`

The line must intersect the x-axis at x=0 and x=-4.

This corresponds to the x-intercepts in Graph C.

Graph C is the correct graph.