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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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Presentation Transcript
how to sketch the graph of an equation
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
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
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
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
x 2 y 2 9
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
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 life1
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
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