Identifying Systems of Inequalities from Graphs: Parabola and Absolute Value

Published on October 19, 2026

Algebra

This problem involves determining the correct system of inequalities based on a graph showing a shaded region bounded by a solid parabola and a dashed absolute value function. The solution requires analyzing the line types (solid vs. dashed) to determine strict or non-strict inequalities and identifying the equations of the boundary curves.

Question

Answer

Step 1 – Identify the parabola.
The solid curve is an upward‑opening parabola with vertex

, so its equation is

. Because the parabola is drawn as a solid line, the inequality is non‑strict (

or

). The shaded region lies above the parabola, so

Step 2 – Identify the absolute‑value graph.
The dashed curve is an inverted “V” with vertex

and slopes

, i.e.

. Because it is drawn dashed, the inequality is strict (

or

). The shaded region lies below this V, so

Step 3 – Combine and compare with option A.
The correct system is

Option A has the strict/non‑strict signs reversed relative to the line styles (it uses

for the solid parabola and

for the dashed V), so A is not correct.

Final answer: the system is

and

(the choice matching these signs, not A).

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