Graphing Parametric Equations Graphing Parametric Equations Suppose that

Graphing Parametric Equations:

Graphing Parametric Equations: Suppose that the system of parametric equations given below represents the path that a figure-skater carves on the ice:

Graphing Parametric Equations: Suppose that the system of parametric equations given below represents the path that a figure-skater carves on the ice: Let’s sketch a graph of the figure-skater’s movement. We can start by constructing a table of values so that we can find ordered pairs on the graph of the system of parametric equations.

Graphing Parametric Equations: To construct a table of values for the system

Graphing Parametric Equations: To construct a table of values for the system let’s choose values for t

Graphing Parametric Equations: t To construct a table of values for the system let’s choose values for t

Graphing Parametric Equations: t To construct a table of values for the system let’s choose values for t, find corresponding values of x(t)

Graphing Parametric Equations: t x(t) To construct a table of values for the system let’s choose values for t, find corresponding values of x(t)

Graphing Parametric Equations: t x(t) To construct a table of values for the system let’s choose values for t, find corresponding values of x(t) and y(t),

Graphing Parametric Equations: t x(t) y(t) To construct a table of values for the system let’s choose values for t, find corresponding values of x(t) and y(t),

Graphing Parametric Equations: t x(t) y(t) To construct a table of values for the system let’s choose values for t, find corresponding values of x(t) and y(t), and then plot ordered pairs (x(t), y(t))

Graphing Parametric Equations: t x(t) y(t) (x(t), y(t) ) To construct a table of values for the system let’s choose values for t, find corresponding values of x(t) and y(t), and then plot ordered pairs (x(t), y(t))

Graphing Parametric Equations: t x(t) y(t) (x(t), y(t) ) To construct a table of values for the system let’s choose values for t, find corresponding values of x(t) and y(t), and then plot ordered pairs (x(t), y(t)) on a coordinate plane.

Graphing Parametric Equations: t x(t) y(t) (x(t), y(t) ) To construct a table of values for the system let’s choose values for t, find corresponding values of x(t) and y(t), and then plot ordered pairs (x(t), y(t)) on a coordinate plane.

Graphing Parametric Equations: t x(t) y(t) (x(t), y(t) )

Graphing Parametric Equations: t x(t) y(t) (x(t), y(t) ) Let’s start with t = 0.

Graphing Parametric Equations: t 0 x(t) y(t) (x(t), y(t) ) Let’s start with t = 0.

Graphing Parametric Equations: t 0 x(t) y(t) (x(t), y(t) ) Let’s start with t = 0. Then

Graphing Parametric Equations: t 0 x(t) 0 y(t) (x(t), y(t) ) Let’s start with t = 0. Then

Graphing Parametric Equations: t 0 x(t) 0 y(t) (x(t), y(t) ) Let’s start with t = 0. Then and

Graphing Parametric Equations: t 0 x(t) 0 y(t) 8 (x(t), y(t) ) Let’s start with t = 0. Then and

Graphing Parametric Equations: t 0 x(t) 0 y(t) 8 (x(t), y(t) ) Let’s start with t = 0. Then and So (0, 8) is on the graph of this system.

Graphing Parametric Equations: t 0 x(t) 0 y(t) 8 (x(t), y(t) ) (0, 8) Let’s start with t = 0. Then and So (0, 8) is on the graph of this system.

Graphing Parametric Equations: t 0 x(t) 0 y(t) 8 (x(t), y(t) ) (0, 8) Let’s start with t = 0. Then and So (0, 8) is on the graph of this system. Let’s plot this point on our coordinate plane.

Graphing Parametric Equations: t 0 x(t) 0 y(t) 8 (x(t), y(t) ) (0, 8)

Graphing Parametric Equations: t 0 x(t) 0 y(t) 8 (x(t), y(t) ) (0, 8) Now let’s take t = 1.

Graphing Parametric Equations: t 0 x(t) 0 y(t) 8 (x(t), y(t) ) (0, 8) Now let’s take t = 1. 1

Graphing Parametric Equations: t 0 x(t) 0 y(t) 8 1 (x(t), y(t) ) (0, 8) Now let’s take t = 1. Then

Graphing Parametric Equations: t 0 1 x(t) 0 4 y(t) 8 (x(t), y(t) ) (0, 8) Now let’s take t = 1. Then

Graphing Parametric Equations: t 0 1 x(t) 0 4 y(t) 8 (x(t), y(t) ) (0, 8) Now let’s take t = 1. Then and

Graphing Parametric Equations: t 0 1 x(t) 0 4 y(t) 8 5. 7 (x(t), y(t) ) (0, 8) Now let’s take t = 1. Then and

Graphing Parametric Equations: t 0 1 x(t) 0 4 y(t) 8 5. 7 (x(t), y(t) ) (0, 8) Now let’s take t = 1. Then and So (4, 5. 7) is on the graph of this system.

Graphing Parametric Equations: t 0 1 x(t) 0 4 y(t) 8 5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) Now let’s take t = 1. Then and So (4, 5. 7) is on the graph of this system.

Graphing Parametric Equations: t 0 1 x(t) 0 4 y(t) 8 5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) Now let’s take t = 1. Then and So (4, 5. 7) is on the graph of this system. Let’s plot this point on our coordinate plane

Graphing Parametric Equations: t 0 1 x(t) 0 4 y(t) 8 5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) Now let’s take t = 1. Then and So (4, 5. 7) is on the graph of this system. Let’s plot this point on our coordinate plane and connect our points.

Graphing Parametric Equations: t 0 1 x(t) 0 4 y(t) 8 5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7)

Graphing Parametric Equations: t 0 1 x(t) 0 4 y(t) 8 5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) Now let’s take t = 2.

Graphing Parametric Equations: t 0 1 x(t) 0 4 y(t) 8 5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) Now let’s take t = 2. 2

Graphing Parametric Equations: t 0 1 x(t) 0 4 y(t) 8 5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) Now let’s take t = 2. Then 2

Graphing Parametric Equations: t 0 1 2 x(t) 0 4 0 y(t) 8 5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) Now let’s take t = 2. Then

Graphing Parametric Equations: t 0 1 2 x(t) 0 4 0 y(t) 8 5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) Now let’s take t = 2. Then and

Graphing Parametric Equations: t 0 1 2 x(t) 0 4 0 y(t) 8 5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) Now let’s take t = 2. Then and

Graphing Parametric Equations: t 0 1 2 x(t) 0 4 0 y(t) 8 5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) Now let’s take t = 2. Then and So (0, 0) is on the graph of this system.

Graphing Parametric Equations: t 0 1 2 x(t) 0 4 0 y(t) 8 5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) Now let’s take t = 2. Then and So (0, 0) is on the graph of this system.

Graphing Parametric Equations: t 0 1 2 x(t) 0 4 0 y(t) 8 5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) Now let’s take t = 2. Then and So (0, 0) is on the graph of this system. Let’s plot this point on our coordinate plane

Graphing Parametric Equations: t 0 1 2 x(t) 0 4 0 y(t) 8 5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) Now let’s take t = 2. Then and So (0, 0) is on the graph of this system. Let’s plot this point on our coordinate plane and connect our points.

Graphing Parametric Equations: t 0 1 2 x(t) 0 4 0 y(t) 8 5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0)

Graphing Parametric Equations: t 0 1 2 x(t) 0 4 0 y(t) 8 5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) Now let’s take t = 3.

Graphing Parametric Equations: t 0 1 2 x(t) 0 4 0 y(t) 8 5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) Now let’s take t = 3. 3

Graphing Parametric Equations: t 0 1 2 x(t) 0 4 0 y(t) 8 5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) Now let’s take t = 3. Then 3

Graphing Parametric Equations: t 0 1 2 3 x(t) 0 4 0 -4 y(t) 8 5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) Now let’s take t = 3. Then

Graphing Parametric Equations: t 0 1 2 3 x(t) 0 4 0 -4 y(t) 8 5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) Now let’s take t = 3. Then and

Graphing Parametric Equations: t 0 1 2 3 x(t) 0 4 0 -4 y(t) 8 5. 7 0 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) Now let’s take t = 3. Then and

Graphing Parametric Equations: t 0 1 2 3 x(t) 0 4 0 -4 y(t) 8 5. 7 0 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) Now let’s take t = 3. Then and So (-4, -5. 7) is on the graph of this system.

Graphing Parametric Equations: t 0 1 2 3 x(t) 0 4 0 -4 y(t) 8 5. 7 0 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) Now let’s take t = 3. Then and So (-4, -5. 7) is on the graph of this system.

Graphing Parametric Equations: t 0 1 2 3 x(t) 0 4 0 -4 y(t) 8 5. 7 0 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) Now let’s take t = 3. Then and So (-4, -5. 7) is on the graph of this system. Let’s plot this point on our coordinate plane

Graphing Parametric Equations: t 0 1 2 3 x(t) 0 4 0 -4 y(t) 8 5. 7 0 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) Now let’s take t = 3. Then and So (-4, -5. 7) is on the graph of this system. Let’s plot this point on our coordinate plane and connect our points.

Graphing Parametric Equations: t 0 1 2 3 x(t) 0 4 0 -4 y(t) 8 5. 7 0 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7)

Graphing Parametric Equations: t 0 1 2 3 x(t) 0 4 0 -4 y(t) 8 5. 7 0 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) Now let’s take t = 4.

Graphing Parametric Equations: t 0 1 2 3 x(t) 0 4 0 -4 y(t) 8 5. 7 0 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) Now let’s take t = 4. 4

Graphing Parametric Equations: t 0 1 2 3 x(t) 0 4 0 -4 y(t) 8 5. 7 0 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) Now let’s take t = 4. Then 4

Graphing Parametric Equations: t 0 1 2 3 4 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) Now let’s take t = 4. Then

Graphing Parametric Equations: t 0 1 2 3 4 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) Now let’s take t = 4. Then and

Graphing Parametric Equations: t 0 1 2 3 4 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 -8 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) Now let’s take t = 4. Then and

Graphing Parametric Equations: t 0 1 2 3 4 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 -8 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) Now let’s take t = 4. Then and So (0, -8) is on the graph of this system.

Graphing Parametric Equations: t 0 1 2 3 4 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 -8 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) Now let’s take t = 4. Then and So (0, -8) is on the graph of this system.

Graphing Parametric Equations: t 0 1 2 3 4 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 -8 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) Now let’s take t = 4. Then and So (0, -8) is on the graph of this system. Let’s plot this point on our coordinate plane

Graphing Parametric Equations: t 0 1 2 3 4 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 -8 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) Now let’s take t = 4. Then and So (0, -8) is on the graph of this system. Let’s plot this point on our coordinate plane and connect our points.

Graphing Parametric Equations: t 0 1 2 3 4 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 -8 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8)

Graphing Parametric Equations: t 0 1 2 3 4 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 -8 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) Now let’s take t = 5.

Graphing Parametric Equations: t 0 1 2 3 4 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 -8 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) Now let’s take t = 5. 5

Graphing Parametric Equations: t 0 1 2 3 4 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 -8 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) Now let’s take t = 5. Then 5

Graphing Parametric Equations: t 0 1 2 3 4 5 x(t) 0 4 0 -4 0 4 y(t) 8 5. 7 0 -5. 7 -8 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) Now let’s take t = 5. Then

Graphing Parametric Equations: t 0 1 2 3 4 5 x(t) 0 4 0 -4 0 4 y(t) 8 5. 7 0 -5. 7 -8 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) Now let’s take t = 5. Then and

Graphing Parametric Equations: t 0 1 2 3 4 5 x(t) 0 4 0 -4 0 4 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) Now let’s take t = 5. Then and

Graphing Parametric Equations: t 0 1 2 3 4 5 x(t) 0 4 0 -4 0 4 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) Now let’s take t = 5. Then and So (4, -5. 7) is on the graph of this system.

Graphing Parametric Equations: t 0 1 2 3 4 5 x(t) 0 4 0 -4 0 4 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) Now let’s take t = 5. Then and So (4, -5. 7) is on the graph of this system.

Graphing Parametric Equations: t 0 1 2 3 4 5 x(t) 0 4 0 -4 0 4 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) Now let’s take t = 5. Then and So (4, -5. 7) is on the graph of this system. Let’s plot this point on our coordinate plane

Graphing Parametric Equations: t 0 1 2 3 4 5 x(t) 0 4 0 -4 0 4 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) Now let’s take t = 5. Then and So (4, -5. 7) is on the graph of this system. Let’s plot this point on our coordinate plane and connect our points.

Graphing Parametric Equations: t 0 1 2 3 4 5 x(t) 0 4 0 -4 0 4 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7)

Graphing Parametric Equations: t 0 1 2 3 4 5 x(t) 0 4 0 -4 0 4 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) Now let’s take t = 6.

Graphing Parametric Equations: t 0 1 2 3 4 5 x(t) 0 4 0 -4 0 4 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) Now let’s take t = 6. 6

Graphing Parametric Equations: t 0 1 2 3 4 5 x(t) 0 4 0 -4 0 4 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) Now let’s take t = 6. Then 6

Graphing Parametric Equations: t 0 1 2 3 4 5 6 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) Now let’s take t = 6. Then

Graphing Parametric Equations: t 0 1 2 3 4 5 6 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) Now let’s take t = 6. Then and

Graphing Parametric Equations: t 0 1 2 3 4 5 6 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) Now let’s take t = 6. Then and

Graphing Parametric Equations: t 0 1 2 3 4 5 6 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) Now let’s take t = 6. Then and So (0, 0) is on the graph of this system.

Graphing Parametric Equations: t 0 1 2 3 4 5 6 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) (0, 0) Now let’s take t = 6. Then and So (0, 0) is on the graph of this system.

Graphing Parametric Equations: t 0 1 2 3 4 5 6 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) (0, 0) Now let’s take t = 6. Then and So (0, 0) is on the graph of this system. Let’s plot this point on our coordinate plane and connect our points.

Graphing Parametric Equations: t 0 1 2 3 4 5 6 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) (0, 0)

Graphing Parametric Equations: t 0 1 2 3 4 5 6 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) (0, 0) Now let’s take t = 7.

Graphing Parametric Equations: t 0 1 2 3 4 5 6 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) (0, 0) Now let’s take t = 7. 7

Graphing Parametric Equations: t 0 1 2 3 4 5 6 x(t) 0 4 0 -4 0 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) (0, 0) Now let’s take t = 7. Then 7

Graphing Parametric Equations: t 0 1 2 3 4 5 6 7 x(t) 0 4 0 -4 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) (0, 0) Now let’s take t = 7. Then

Graphing Parametric Equations: t 0 1 2 3 4 5 6 7 x(t) 0 4 0 -4 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 0 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) (0, 0) Now let’s take t = 7. Then and

Graphing Parametric Equations: t 0 1 2 3 4 5 6 7 x(t) 0 4 0 -4 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 0 5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) (0, 0) Now let’s take t = 7. Then and

Graphing Parametric Equations: t 0 1 2 3 4 5 6 7 x(t) 0 4 0 -4 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 0 5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) (0, 0) Now let’s take t = 7. Then and So (-4, 5. 7) is on the graph of this system.

Graphing Parametric Equations: t 0 1 2 3 4 5 6 7 x(t) 0 4 0 -4 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 0 5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) (0, 0) (-4, 5. 7) Now let’s take t = 7. Then and So (-4, 5. 7) is on the graph of this system.

Graphing Parametric Equations: t 0 1 2 3 4 5 6 7 x(t) 0 4 0 -4 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 0 5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) (0, 0) (-4, 5. 7) Now let’s take t = 7. Then and So (-4, 5. 7) is on the graph of this system. Let’s plot this point on our coordinate plane

Graphing Parametric Equations: t 0 1 2 3 4 5 6 7 x(t) 0 4 0 -4 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 0 5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) (0, 0) (-4, 5. 7) Now let’s take t = 7. Then and So (-4, 5. 7) is on the graph of this system. Let’s plot this point on our coordinate plane and connect our points.

Graphing Parametric Equations: t 0 1 2 3 4 5 6 7 x(t) 0 4 0 -4 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 0 5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) (0, 0) (-4, 5. 7)

Graphing Parametric Equations: t 0 1 2 3 4 5 6 7 x(t) 0 4 0 -4 y(t) 8 5. 7 0 -5. 7 -8 -5. 7 0 5. 7 (x(t), y(t) ) (0, 8) (4, 5. 7) (0, 0) (-4, -5. 7) (0, -8) (4, -5. 7) (0, 0) (-4, 5. 7) Finally, we can finish our graph. We can now see that the figure skater carved a figure-eight on the ice.