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Section P.2

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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Section P.2

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  1. Group C Section P.2

  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

  3. Example 1 First, make a table of values by choosing values of x and calculating the values of y Now plot the corresponding points

  4. 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

  5. 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

  6. 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.

  7. 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?

  8. 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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