Precalculus Pre-AP SUMMER 2015. Defining a Function When defining a function, we use coordinate points… ( x, y ) Typically, we use “x” to find out.

Precalculus Pre-APSUMMER 2015

Defining a Function

When defining a function, we use coordinate points… ( x , y )

Typically, we use “x” to find out the value of “y”, and vice versa.

Defining a Function…Parametrically

Up until this point, we’ve used equations to tell us the values of x and y.

Today, we’ll examine what it would look like if x and y were defined by equations using a THIRD variable t. This is called a parameter.

Parametric Equations

Why…

Some functions and graphs can best be defined parametrically, rather than only using x and y.


ExampleX and Y are defined by the equations…

x = t + 1

y = t2 + 2t

Find the points determined by…

t = -3, -2, -1, 0, 1, 2, and 3.


ExampleX and Y are defined by the equations…

x = t + 1

y = t2 + 2t

Find an algebraic relationship between x and y. This is often called (“eliminating the parameter”).

Is this relationship a function?


Pg. 135# 1-8

Applications of Parametric Equations

Remember projectile motion from Algebra 2…

y = -16t2 + v0t + y0

Applications of Parametric Equations

Remember projectile motion from Algebra 2…

y = -16t2 + v0t + y0

This was okay, but what DIDN’T we account for with this equation?

Projectile Motion… Version 2.0!!!

Here is how we’ll think about it now…

X represents horizontal motion.

Y represents vertical motion.


is the angle made with the horizontal

is the gravity constant

is the initial height


Example 1

A golf ball is hit at an angle of 65o with an initial velocity of 71 feet per second.

Write a set of parametric equations to represent this situation.

What is the maximum height of the ball?


Example 1


How long was the ball in the air?

How far has the ball traveled horizontally before it hits the ground?


Example 1


How high was the ball after 1.1 seconds?


Example 2

A rock is thrown off of a 121 meter cliff at an angle of 43 degrees. The initial velocity is 28 meters per second.

Write a set of parametric equations to represent this situation.

What is the maximum height of the rock?


Example 2


How long was the rock in the air?

How far did the rock travel horizontally before it hit the ground?


Example 2


How high was the ball after 0.6 seconds?

Precalculus Pre-AP SUMMER 2015. Defining a Function When defining a function, we use coordinate points… ( x, y ) Typically, we use “x” to find out.

Documents

equations x

parametric equations

set of parametric equations

projectile motion version

value of y

initial velocity

values of x

golf ball