# Designing a Roller coaster

## Summary

Our roller coaster's name is Snap Crackle and Pop. How we created the roller coaster was that as we went through each section we tried to use a function that would create that part of the roller coaster. As we pictured on how our roller coaster should look like, we would connect some of the functions to the roller coaster. We would look at the functions characteristics and compare it to the roller coaster and try to make an equation for it. The difficulty we had when creating our roller coaster and coming up with an equation for each section of coaster was trying to figure out that right stretches and compression on the y and x-axis. It was easier to make the equations for the drops using the vertex form when it was a function with the degree of 2 and 4.

## Height Vs. Time

In the beginning, as time increases the height also increases. At 25 seconds, the roller coaster reaches its maximum height at 300 feet. Then as time goes forward to 32 seconds, height decreases and it continues down as a drop down a parabola. Afterwards, height increases and decreases giving the drop feeling in a roller coaster.

## EQUATIONS AND RESTRICTIONS

1. y= 10 Domain: {0<x<5.68}

2. y= 15(x-5) Domain: {5<x<25.001} Range: {10<y}

3. y= -5(x-25)^2 + 300 Domain: {25<x<32}

4. y= 235sin(x-32) + 55 Domain: {32<x<33.57}

5. y= -(x-33.57)^4 + 290 Domain: {33.57<x<43.5} Range: {20<y}

6. y= (x-37)^4 + 20 Domain: {37.62<x<41}

7. y= -(x-41)^2 + 276 Domain: {41<x<57} Range: {20<y}

8. x= -2^{-(y-20)} + 58 Domain: {57<x} Range: {y<251}

9. x= 12log(-y+251) + 58 Domain: {86.406<y<250}Range: {x<86.406}

10. x= -0.1(y-87) + 84.59Range: {10<y<87}

11. y= 10 Domain: {92.3<x<100}