SECTION P.2Group C

How to Sketch the Graph of an Equation Graph of Equation: The set of

all solution points of an equation

1. Rewrite the equation so that one of the variables is isolated on one side

2. Make a table of several solution points

3. Plot these points in the Cartesian plane

4. Connect the points with a smooth curve

Example 1

x -2 -1 0 1 2 3

y=x2-2 2 -1 -2 -1 2 7

First, make a table of values by choosing values of x and calculating the values of y

Now plot the corresponding points

x

y

Using a Graphing Utility

1. Rewrite the equation so y is isolated

2. Enter the equation into the utility

3. Determine a viewing window that shows all important features of the graph

4. Graph equation

Example 2: Sketching a Circle Using a Graphing Utility

The graph of x2 + y2 = 9 is a circle whose center is at the origin and radius is 3. To graph the equation, solve for y.

x2 + y2 = 9 y2 = 9 - x2

y = √9 - x2

The graph of y = √9 - x2 is the top half The graph of y = -√9 - x2 is the bottom

half

x2 + y2 = 9

x

yEnter both equations into the calculator and generate the graph. If you use the standard viewing window the graph may not appear to be a circle, by changing the viewing window to a square setting you can overcome this.

Example 3: Real life

A runner runs a constant rate of 4.9 mph. (Distance = Rate x Time)

d = 4.9t

a) Determine how far a runner can run in 3.1 hours

b) How long will it take to run a 26.2 mile marathon?

Example 3: Real life

a) Substitute 3.1 hours for td = 4.9(3.1)d = 15.2 milesIn 3.1 hours the runner could run 15.2 miles

b) d = Rtd/R = t26.2m / 4.9mph = tt = 5.3 hours

It would take about 5.3 hours to run a 26.2 mile marathon