example 5 Graphical Solutions

Chapter 2.1

Solve for x using the x-intercept method.2 3

14 3

x x

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Solve for x using the x-intercept method.2 3

14 3

x x

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Solve for x using the x-intercept method.2 3

14 3

x x

2 30 1

3 4

x x 2 3

13 4

x xy

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Solve for x using the x-intercept method.2 3

14 3

x x

2 30 1

3 4

x x 2 3

13 4

x xy

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Solve for x using the x-intercept method.2 3

14 3

x x

2 30 1

3 4

x x 2 3

13 4

x xy

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Solve for x using the x-intercept method.2 3

14 3

x x

2 30 1

3 4

x x 2 3

13 4

x xy

2 31

4 32 10.5 3 10.5

14 3

18 13.5

4 34.5 4.5

x x

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Solve for x using the x-intercept method.2 3

14 3

x x

2 30 1

3 4

x x 2 3

13 4

x xy

2 31

4 32 10.5 3 10.5

14 3

18 13.5

4 34.5 4.5

x x

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Solve for x using the x-intercept method.2 3

14 3

x x

2 30 1

3 4

x x 2 3

13 4

x xy

2 31

4 32 10.5 3 10.5

14 3

18 13.5

4 34.5 4.5

x x

2009 PBLPathways

Solve for x using the x-intercept method.2 3

14 3

x x

2 30 1

3 4

x x 2 3

13 4

x xy

2 31

4 32 10.5 3 10.5

14 3

18 13.5

4 34.5 4.5

x x

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Enter the Equation 1.Use the key to enter the function as Y1 . Note that the parentheses in the second term are essential.

2.Make sure that all other functions and plots are turned off.

Set the Window

3.Use the key to set the window as shown.

4.Set Xscl =1 and Yscl =1.

2 31

4 3

x x

/ 3 1 (2 3) / 4x x

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Graph the equation and use TRACE to estimate the zero

5.Press the key to see the graph.

6.Press to see the equation and a point on the graph.

7.Use the right arrow key and the left arrow key to get close to the x-intercept. Here the x-intercept is close to x = 10.5

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Find the x-intercept

8.Press to access CALC. A CALCULATE screen appears.

9.Press the key or cursor down to 2: zero and press .

10.You are brought back to the graph screen.

11.You must select a Left Bound to tell the calculator where to look for the x-intercept. To do this, move the cursor somewhere close to the left side of the x-intercept. Press .

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12. Notice that an arrow appears at the top of the screen above your left bound. This is the left bound of the interval that contains the x-intercept.

13. You must select a Right Bound to tell the calculator where to look for the x-intercept. To do this, move the cursor somewhere close to the right side of the x-intercept. Press .

14. Notice that an arrow appears at the top of the screen above your right bound. This is the right bound of the interval that contains the x-intercept.

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15. Next, you must enter a Guess. You can enter a value somewhere within the interval defined by your left and right bounds

16. Finally, press to see the coordinates of the x-intercept at the bottom of the screen.

17. Note that the TI-83 and TI-83 PLUS call the x-intercept a Zero. This x-value matches the algebraic solution.

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Enter the Equation

1.Use the key to enter the left side of the function as Y1 and the right side of the function as Y2 .

2. Note that the parentheses in the numerator of Y1 are essential. Set the Window

3.Use the key to set the window as shown.

4.Set Xscl=1 and Yscl=1.

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Graph the equations

5.Press the key to see the graphs.

6.Press to see the equation of one of the lines. Use the up or down arrow to see the equation of the second line.

7.Use the right arrow key to get close to the intersection point of the two lines. Note that using does not necessarily give the exact coordinates of the intersection point.

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Find the exact coordinates of the intersection point

8.Press to access CALC. A CALCULATE screen appears.

9.Press the key or cursor down to 5:intersect and press .

10.You are brought back to the graph screen.

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11. You must select a First curve to tell the calculator which of the lines you want to use for the intersection. Press .

12. Next you must select a Second curve to tell the calculator which second curve to use for the intersection. Use the up or down arrow key to move to the other line. Press .

13. Next you must enter a Guess. Position the cursor near the point of intersection.

14. Finally, press to see the coordinates of the Intersection at the bottom of the screen.