you are correct here. this is a polynomial and so the domain is everywhere, that is,

the graph is an upside down parabola, with vertex (-1,2) and x-intercepts

the triangle is right-isosceles, so the line AB has the same length as the line from (-1,0) to B. thus, by Pythagoras, if we call the length of AB, , then we have thattriangle question>

http://i207.photobucket.com/albums/b..._/untitled.jpg

Now we can find another right triangle, ABO, again by Pythagoras, we can find the length of OB. We find that this is 1. therefore, B is the point (0,1).

From this we can deduce that AB is a segment of the line

Therefore, the point P is given by , so the y-coordinate in terms of x is 1 - x. and that takes care of part (a)

for (b), the answer is now obvious. the area of a rectangle is length times width. the width, which i take to be the height if given by (1 - x), the length is the base which is 2x, thus we have: