Andrew is the first-grade class make paper trees. for each student, he folds a rectangular piece of construction paper in half lengthwise. then, he cuts the folded paper into a triangular shape with the same base and height a the rectangle. then he unfolds the paper and throws away the scraps. the original piece of paper is 11inches by 8.5 inches. area of paper thrown away per student:

Okay, not too hard.  So, we have 11 inches by 8.5 inches.

If Andrew is to fold the paper in half lengthwise, this would mean that it would affect the width (8.5 inches).  So after the fold.  It is now 11 inches by 4.25 inches.

The question is vague but if it is talking about cutting both pieces of the paper after the fold, the base is 4.25 and the height is 11.  This will make two right triangles with a height of 11 and a base of 2.125.

The formula for area is 1/2bh but since there are two triangles, we can cancel out the 1/2 and only take the base times the height which would be 2.125 * 11.  This in turn would be 23.375in².  However, since it is on two pieces of folded paper, you would multiply that by 2 and get 23.375 * 2 = 46.75in² of wasted paper.

Answer is 46.75in²

The vertex of the quadratic function is (1.5, -.75)