### Home > APCALC > Chapter 2 > Lesson 2.1.2 > Problem 2-23

Kristin is designing a model that will represent the path of a roller coaster. She has determined the beginning and the end parts of the track, but needs to write a formula for the middle section that will join the other segments. She decides that she wants one peak in this middle section, not including its boundaries. What values of * *and

*will make her model, given below, a continuous function? To help you visualize this, use the*

Sara's roller coaster needs to be continuous. That means that the -values at the boundary points

Determine the -value of the roller coaster at

Next, determine the -value of the roller coaster at

We are ready to find the equation of the middle piece of the piecewise function. This piece has two unknowns, and

*. Fortunately, in Step 2 and Step 3, we found two values that exist on the middle equation, if the piecewise is continuous.*

Write and solve a system for

*and*

*:*

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Click the link at right for the full version of the eTool: *Calc 2-23 HW eTool*