Section P.2

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# Section P.2 - PowerPoint PPT Presentation

Group C. Section P.2. How to Sketch the Graph of an Equation. Graph of Equation: The set of all solution points of an equation Rewrite the equation so that one of the variables is isolated on one side Make a table of several solution points Plot these points in the C artesian plane

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## PowerPoint Slideshow about ' Section P.2' - lars

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Presentation Transcript
Group C

### Section P.2

How to Sketch the Graph of an Equation
• Graph of Equation: The set of all solution points of an equation
• Rewrite the equation so that one of the variables is isolated on one side
• Make a table of several solution points
• Plot these points in the Cartesian plane
• Connect the points with a smooth curve
Example 1

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

Now plot the corresponding points

Using a Graphing Utility
• Rewrite the equation so y is isolated
• Enter the equation into the utility
• Determine a viewing window that shows all important features of the graph
• 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

Enter 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
• Determine how far a runner can run in 3.1 hours
• How long will it take to run a 26.2 mile marathon?
Example 3: Real life
• Substitute 3.1 hours for t
• d = 4.9(3.1)
• d = 15.2 miles
• In 3.1 hours the runner could run 15.2 miles
• d = Rt
• d/R = t
• 26.2m / 4.9mph = t
• t = 5.3 hours
• It would take about 5.3 hours to run a 26.2 mile marathon