Question

which graph displays a quadratic equation with the solutions -2 and -4? image created with desmos.

Explanation:

Step1: Recall roots of quadratic

If a quadratic has solutions (roots) at \( x = -2 \) and \( x = -4 \), then the factors are \( (x + 2) \) and \( (x + 4) \). The quadratic equation is \( y=(x + 2)(x + 4) \) or expanded \( y=x^{2}+6x + 8 \). The graph of a quadratic (parabola) intersects the x - axis at its roots. So we need a parabola that crosses the x - axis at \( x=-2 \) and \( x = -4 \).

Step2: Analyze the given graph

Looking at the provided graph, we check the x - intercepts (where \( y = 0 \)). The graph shown crosses the x - axis at \( x=-4 \) and \( x=-2 \), which matches the roots we need for the quadratic with solutions - 2 and - 4. The other option (the one with the vertical line, which is not a parabola) can't be a quadratic graph. So the graph shown (the parabola intersecting x - axis at - 4 and - 2) is the correct one.

Answer:

The graph (the parabola) that intersects the x - axis at \( x=-4 \) and \( x = -2 \) (the one with the U - shaped curve crossing the x - axis at - 4 and - 2)