The region  contains only  values which are greater than or equal to those on the line , so its  values are .

Similarly, the region contains only  values which are less than or equal to those on the line , so its  values are .

To begin, we analyze the equation given: the base equation,  is shifted left one unit and vertically stretched by a factor of 2. The graph of the equation  is:

To solve the inequality, we need to take a test point and plug it in to see if it matches the inequality. The only points that cannot be used are those directly on our parabola, so let's use the origin . If plugging this point in makes the inequality true, then we shade the area containing that point (in this case, outside the parabola); if it makes the inequality untrue, then the opposite side is shaded (in this case, the inside of the parabola). Plugging the numbers in shows:

Simplified as:

Which is not true, so the area inside of the parabola should be shaded, resulting in the following graph:

The equation for a circle centered at point  with radius  is . Our circle is centered at  with , and we are interested in points that lie along or inside of the circle. This means the left-hand side must be less than or equal to the right-hand side of the equation. We are left with  or 

This is a graph of a circle with radius of 5 and a center of (1,1). The center of the circle is not on the edge of the circle, so that is the correct answer. All other points are exactly 5 units away from the circle's center, making them a part of the circle.

The center of the circle is , so plugging those values in for x and y yields the response that 0 is greater than or equal to 25.

Since plugging in the center values gives us a false statement we know that our center does not satisfy the inequality. 

Check the center of the circle to see if that point satisfies the inequality.

When evaluating the function at the center (1,1), we see that it does not satisfy the equation, so it cannot be in the shaded region of the graph.

Therefore the shading is outside of the circle.

This is a graph of a circle with radius of 6 and a center of (-2,4). The point (2,2) is not on the edge of the circle, so that is the correct answer. All other points are exactly 6 units away from the circle's center, making them a part of the circle.

The left side of the equation must be greater than or equal to 36 in order to satisfy the equation, so plugging in each of the values for x and y, we see:

Therefore only  yields an answer that is greater than or equal to 36.

The center of the circle is , so plugging those values in for x and y yields the response,

Therefore, the center does not satisfy the inequality. 

Check the center of the circle to see if that point satisfies the inequality. When evaluating the function at the center (-2,4), we see that it does not satisfy the equation, so it cannot be in the shaded region of the graph. Therefore the shading is outside of the circle.