Any idea how to do this quadratic function question?

a) The square has side length C. Therefore, its area is C². The area of the shaded region, therefore, is the area of the rectangle minus the area of the square.

A = 25×16 − C² = 400 − C²

b) We're looking for the value of C such that the area of the square is the largest. If no part of the square can lie outside the rectangle, this can only be accomplished when C is equal to the smallest side length of the rectangle. Hence, the maximum possible value of C is 16.

c) Press [Y=] and type into Y1: 400−X². Press [Window] and use the following dimensions:

Xmin = 0

Xmax = 20

Ymin = 0

Ymax = 400

Pretend in this case, Y1 is A and X is C. As you can see, when C = 0 (the square does not exist), the rectangle will have the most area. As C increases, the area of the rectangle decreases. If the restriction that the square cannot be found outside the rectangle applies, then the least amount of area will be when C=16.

d) The equation A = 400 − C² itself has a domain of all real numbers and an image of all real numbers less than or equal to 400. In the context of the problem, however, it should have a domain of 0 ≤ C ≤ 20 (since C, a side length, cannot be negative nor exceed a length of 20), while the image should be 0 ≤ A ≤ 400, since you cannot have a negative area or an area larger than 400.