1. Sullivan Algebra and Trigonometry: Section 11.7 Objectives of this Section Graph Parametric Equations Find a Rectangular Equation for a Curve Defined Parametrically Use Time as a Parameter in Parametric Equations Find Parametric Equations for Curves Defined by Rectangular Equations

2. Let x = f(t) and y = g(t), where f and g are two functions whose common domain is some interval I. The collection of points defined by (x, y) = (f(t), g(t)) is called a plane curve. The equations x = f(t) y = g(t) where t is in I, are called parametric equations of the curve. The variable t is called a parameter.

4. (4,0) (1,1) (0, 2) (1, 3) (4, 4)

5. Parabola with vertex at (0, 2) that opens to the right.

7. Randy Johnson throws a baseball with an initial speed of 130 feet per second at an angle of 10 degrees to the horizontal. The ball leaves Randy Johnson’s hand at a height of 6 feet. (a) Find parametric equations that describe the position of the ball as a function of time.

8. (b) How long was the ball in the air? The ball was in the air for about 1.64 seconds.

9. (c) When was the ball at its maximum height? (d) What was the maximum height of the ball?

10. (e) Determine the distance the ball traveled. (f) Use a graphing utility to simulate the motion of the baseball by simultaneously graphing the equations found in (a).