Question

At the state fair, Erin and her cousin ride the Ultra Drop roller coaster. When the ride plummets down the first hill it dips below the loading platform. At the bottom, a camera snaps the rider’s picture before hurtling them back toward the sky.

The equation the roller coaster's path 3x^2-9x+38=2x^2+18 models over time. The variable y represents height (in feet) above or below the platform. At y=0 the roller coaster is even with the platform. The variable x represents the amount of time (in seconds) elapsed since the ride began.

1 Write the equation in standard form. (

2 Write the factored form of the equation you found in Part I.

3 Use the zero product rule to solve the factored form of the equation you found in Part II. Show your work and check your solution(s).

4 What does your answer to Part III tell you about the roller coaster's height at certain points in time?

5 The equation for the roller coaster's path can also be written as y=(x-4.5)^2-0.25

What is the name for this form of the equation? What is the height and time at which Erin's picture is taken during the roller coaster ride?