Questions: Choose the solution (intersection) of this quadratic system of inequalities. x^2 + y^2 ≤ 9 and y ≥ -x^2 + 2

Choose the solution (intersection) of this quadratic system of inequalities.
x^2 + y^2 ≤ 9 and y ≥ -x^2 + 2
Transcript text: Choose the solution (intersection) of this quadratic system of inequalities. \[ x^{2}+y^{2} \leq 9 \text { and } y \geq-x^{2}+2 \]
failed

Solution

failed
failed

Solution Steps

Step 1: Analyze the first inequality

The first inequality, \(x^2 + y^2 \le 9\), represents the area inside and on a circle centered at the origin with a radius of 3.

Step 2: Analyze the second inequality

The second inequality, \(y \ge -x^2 + 2\), represents the area above and on the parabola \(y = -x^2 + 2\), which opens downwards and has a vertex at (0, 2).

Step 3: Find the intersection

The solution to the system of inequalities is the intersection of the regions defined by each inequality. This is the region that lies inside or on the circle and is also above or on the parabola. This corresponds to the second option.

Final Answer

The second graph is the correct answer.

Was this solution helpful?
failed
Unhelpful
failed
Helpful