(1.5 points) You are designing part of a roller coaster with two pieces of rails that...

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(1.5 points) You are designing part of a roller coaster with two pieces of rails that are part of two parabolas. The first piece starts at the top of the track at height 40 meter and ends after it travels a horizontal distance 16 meters. The height of the first piece is modeled by equation y = 40-0.1x² as a function of horizontal distance, z, in meters. The next piece starts at the end of the first piece and ends on the ground level as seen in the picture. The height of the second piece is modeled by equation y = a(z-b)² where a and b are constants. height { 16 b (a) Use the given formula for each piece to fill in the blanks and write the piecewise defined function that models your design. f(x) = X if 0 ≤ x ≤ 16 if 16 < x (1.5 points) You are designing part of a roller coaster with two pieces of rails that are part of two parabolas. The first piece starts at the top of the track at height 40 meter and ends after it travels a horizontal distance 16 meters. The height of the first piece is modeled by equation y = 40-0.1x² as a function of horizontal distance, z, in meters. The next piece starts at the end of the first piece and ends on the ground level as seen in the picture. The height of the second piece is modeled by equation y = a(z-b)² where a and b are constants. height { 16 b (a) Use the given formula for each piece to fill in the blanks and write the piecewise defined function that models your design. f(x) = X if 0 ≤ x ≤ 16 if 16 < x