(a) A photographer captured a photo as shown in Figure A below. Later, he discovered that the line which joins the bottom and the top of the mountain and the line which joins the top of the mountain and the aeroplane form a 90° angle, that is,

The roller coaster is 80 feet above the ground at a horizontal position of 110 feet from the boarding station.The roller coaster is at a height of 100 feet above the ground as it descends the hill and reaches a horizontal position of 170 feet from the boarding station.The roller coaster levels off at a height of 80 feet above the ground at a horizontal position of 200 feet from the boarding station, then resumes dropping.A drawing of a section of the roller coaster with points marked at 110 comma 80, 170 comma 100, and 200 comma 80.Using the height of 80 feet as a baseline (because that is also the height the roller coaster is when it levels off), determine the rule for the polynomial function representing the height of the roller coaster,  h open parentheses x close parentheses, at a horizontal position of x feet from that of the boarding station. This rule can be left in factored form. Fill in the blanks to report your result as follows. a should be written as an integer or…