Follow these steps to explore a relationship between linear, quadratic, square root, absolute-value, and semicircle functions.
Use friendly windows of an appropriate size.
a. Graph these equations simultaneously on your calculator. The first four functions intersect in the same two points. What are the coordinates of these points?

b. Imagine using the intersection points that you found in 9a to draw a rectangle that just encloses the quarter-circle that is on the right half of the fifth function. How do the coordinates of the points relate to the dimensions of the rectangle?
c. Solve these equations for y and graph them simultaneously on your calculator. Where do the first four functions intersect?

d. Imagine using the intersection points that you found in 9c to draw a rectangle that just encloses the right half of the fifth function. How do the coordinates of the points relate to the dimensions of the rectangle?
e. Solve these equations for y and graph them simultaneously on your calculator. Where do the first four functions intersect?

f. What are the dimensions of a rectangle that encloses the right half of the fifth function?
How do these dimensions relate to the coordinates of the two points in 9e?
g. In each set of functions, one of the points of intersection located the center of the transformed semicircle. How did the other points relate to the shape of the semicircle?

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