1. Write an equation to represent the relationship between the step number, \(n\), and the number of small squares, \(y\).

   Briefly describe how each part of the equation relates to the pattern.

   

   Three rectangles made up of unit squares. The first rectangle is 2 rows of 1 column of unit squares, labeled Step 1. The second rectangle is 4 rows and 2 columns of unit squares, labeled Step 2. The third rectangle is 6 rows and 3 columns of unit squares, labeled Step 3.

2. Is the relationship between the step number and number of small squares quadratic? Explain how you know.

Technology required. A small marshmallow is launched straight up in the air with a slingshot. Function \(h\), given by the equation \(h(t)= 5 + 20t - 5t^2\), describes the height of the marshmallow, in meters, as a function of time, \(t\), in seconds since it was launched.

1. Use graphing technology to graph function \(h\).
2. About when does the marshmallow reach its maximum height?
3. About how long does it take before the marshmallow hits the ground?
4. What domain makes sense for function \(h\) in this situation?

A rock is dropped from a bridge over a river. Which graph could represent the distance fallen, in feet, as a function of time in seconds?

A line on a graph, origin O, with grid. Horizontal axis, time, seconds, scale 0 to 8, by 1’s. Vertical axis, distance fallen, feet, scale 0 to 200, by 20’s. A line passes through the origin and the point 2 comma 96.

A line on a graph, origin O, with grid. Horizontal axis, time, seconds, scale 0 to 8, by 1’s. Vertical axis, distance fallen, feet, scale 0 to 200, by 20’s. A line passes through the point 0 comma 180 and 2 comma 84.

A curve on a graph, origin O, with grid. Horizontal axis, time, seconds, scale 0 to 8, by 1’s. Vertical axis, distance fallen, feet, scale 0 to 200, by 20’s. A curve passes through the origin and the point 2 comma 64.

A curve on a graph, origin O, with grid. Horizontal axis, time, seconds, scale 0 to 8, by 1’s. Vertical axis, distance fallen, feet, scale 0 to 200, by 20’s. A curve passes through the point 0 comma 180 and 2 comma 116.