4 minutes Warm-Up Complete the table by evaluating each expression for the given values of x. x 4x + 3 -6x - 5 -2 -1 1 2.

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4 minutes Warm-Up Complete the table by evaluating each expression for the given values of x. x 4x + 3 -6x - 5 -2 -1 1 2

3.6.1 Parametric Equations Objectives: Graph a pair of parametric equations Write the function represented by a pair of parametric equations

Parametric Equations A pair of parametric equations is a pair of continuous functions that define the x- and y-coordinates of a point in a coordinate plane in terms of a third variable, such as t, called the parameter. Altitude (ft) 3 seconds Horizontal distance (ft)

Example 1 Graph the pair of parametric equations below for t x y -3 -2 -1 1 2 3 (-3) - 1 = -4 -2(-3) + 3 = 9 (-2) - 1 = -3 -2(-2) + 3 = 7 (-1) - 1 = -2 -2(-1) + 3 = 5 (0) - 1 = -1 -2(0) + 3 = 3 (1) - 1 = 0 -2(1) + 3 = 1 (2) - 1 = 1 -2(2) + 3 = -1 (3) - 1 = 2 -2(3) + 3 = -3

Practice Graph the pair of parametric equations for

Example 2 Write the pair of parametric equations as a single equation in x and y. y = -2 + 7 x(t) = 3t - 5 solve for t x = 3t - 5 3t = x + 5

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4 minutes Warm-Up Write the pair of parametric equations as a single equation in x and y. 1) 2)

3.6.2 Parametric Equations Objectives: Graph a pair of parametric equations, and use them to model real-world applications

Example 1 An outfielder throws a softball to the third baseman 290 feet away to stop a runner. The ball is released 6 feet above the ground with a horizontal speed of 75 feet per second and a vertical speed of 44 feet per second. The third baseman’s mitt is held 3 feet above the ground. The following parametric equations describe the path of the ball, where t is the number of seconds after the ball is released: a) When does the ball reach is greatest altitude? b) Can the third baseman catch the ball?

Homework study guide