The graph shows a system of inequalities. Which system is represented in the graph? Oy > x²-2x-3 y > x + 3 Oy < x²-2x-3 y < x + 3 Oy ? x²-2x-3 y ? x + 3 Oy > x²-2x-3 y<x+3
The Correct Answer and Explanation is:
From your description, it sounds like you’re trying to identify a system of inequalities based on a graph. Let’s break down the possible options and the reasoning behind each one.
Understanding the inequalities:
- Oy > x² – 2x – 3: This inequality represents a region above the parabola given by y=x2−2x−3y = x^2 – 2x – 3y=x2−2x−3. This is a parabola that opens upwards, and the inequality indicates that the solution lies above the curve.
- y > x + 3: This is a straight line with slope 1 and a y-intercept of 3. The inequality represents the region above this line.
- Oy < x² – 2x – 3: This inequality represents the region below the parabola y=x2−2x−3y = x^2 – 2x – 3y=x2−2x−3, which is a parabola that opens upwards.
- y < x + 3: This inequality represents the region below the line y=x+3y = x + 3y=x+3.
Interpreting the graph:
- If the graph shows a region above the parabola y=x2−2x−3y = x^2 – 2x – 3y=x2−2x−3 and below the line y=x+3y = x + 3y=x+3, the correct system of inequalities would be:
- Oy > x² – 2x – 3 (Region above the parabola)
- y < x + 3 (Region below the line)
Explanation:
- The graph’s shading indicates which side of the curve or line is included in the solution.
- If the shaded region is above the parabola y=x2−2x−3y = x^2 – 2x – 3y=x2−2x−3, the inequality for the parabola will be y>x2−2x−3y > x^2 – 2x – 3y>x2−2x−3, since the solution is above the curve.
- If the shaded region is below the line y=x+3y = x + 3y=x+3, then the inequality for the line will be y<x+3y < x + 3y<x+3, since the solution is below the line.
Thus, the system represented by the graph is:
- Oy > x² – 2x – 3
- y < x + 3
