Exploring the TI-84 Plus in High School Mathematics

Exploring the TI-84 Plus in High School Mathematics

? 2012 Texas Instruments Incorporated

Materials for Institute Participant*

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Exploring the TI-84 Plus in High School Mathematics

Day One 1. Overview, Logistics, and Introductions 2. Roots of Radical Equations 3. Using Symmetry to Find the Vertex of a Parabola 4. Order Pairs 5. All On The Line 6. App Explorations

Probability Simulation: Binomial Probabilities Transformation Graphing: Graphing Quadratic Functions Inequality Graphing: The Impossible Task CabriTM, Jr.: Diameter and Circumference of a Circle 7. Box Plots & Histograms 8. Square It Up! 9. Carousel Algebra 1: Tri This! Geometry: Measuring Angles in a Quadrilateral Algebra 2: Dilations with Matrices Precalculus: Breaking Up is Not Hard to Do Statistics: Density Curves 10. Reflection

Appendix A. TI-ConnectTM Quick Start Guide B. Memory Management on the TI-84 Plus

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5 11 15 21

29 37 49 57 63 69

77 83 87 95 103

107 115

?2012 Texas Instruments Incorporated

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education.

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Roots Of Radical Equations

5 Name ___________________________ Class ___________________________

Problem 1 ? Square Roots

Solve the equations below by graphing them on the calculator and finding the intersection with the x-axis (if there is one). To find the intersection, follow the steps below.

Note: Each equation has been set equal to zero. If an equation was not equal to zero, the correct algebraic steps would be used to do so.

1. x 3 0

Solution: ________

3. x 2 5 0 Solution: ________

5. x 1 0

Solution: ________

2. 2 x 2 4 0 Solution: ________ 4. 3 x 4 0 Solution: ________ 6. x 2 3 0 Solution: ________

Press o and enter the desired equation.

Press q and select ZStandard to display the graph of the equation. If a larger viewing window is needed, press p and enter the desired values.

To find the location(s) of the zeros (the solution to the equation,) press y / and select 2:zero.

Now, use the arrow keys to move the cursor to: the left of the zero and press ?. the right of the zero and press ?. the guess of the zero's location and press ?.

?2011 Texas Instruments Incorporated

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Roots Of Radical Equations

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Roots Of Radical Equations

Problem 2 ? Cubic Roots Solve the equations below by graphing them and finding the intersection with the x-axis (if there is one).

7. 3 x 2 0 9. 3 x 1 4 0 11. 3 x 2 0

Solution: ________ Solution: ________ Solution: ________

8. 33 x 3 0

Solution: ________

10. 23 x 6 0 Solution: ________

12. 23 x 4 3 0 Solution: ________

Extension John wants to place new ATMs exactly 5 miles (in a straight line) from the bank and at the intersection of two streets. In his city, each block is 1 mile long and his bank is located 1 block east and 2 blocks north of the city center. Use the picture to the right and the distance formula to help you answer the questions below. 13. If he installs a machine 3 blocks north,

how far east/west should the ATM be?

14. If he installs a machine 3 blocks south, how far east/west should the ATM be?

15. If he installs a machine 4 blocks east, how far north/south should the ATM be?

16. If he installs a machine 4 blocks west, how far north/south should the ATM be?

?2011 Texas Instruments Incorporated

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Algebra 2

Roots of Radical Equations

ID: 12214

Time required 15?20 minutes

Activity Overview In this activity, students will solve radical equations graphically. Several square and cubic root equations are given for students to graph and find intersections with the x-axis. Students will also use the distance formula to solve an extension problem.

Topic: Radical Equations Roots Graphing

Distance formula

Teacher Preparation and Notes Students should know how to, graph functions. For the extension problem, students will need to use the distance formula. To download the student and worksheet, go to education.exchange and enter "12214" in the keyword search box.

Associated Materials RootsOfRadicalEquations_Student.doc

Suggested Related Activities To download any activity listed, go to education.exchange and enter the number in the keyword search box. Radical Transformations (TI-84 Plus family) -- 11574 Radical Functions (TI-84 Plus family) -- 8977 Solving Equations with Two Radicals (TI-Nspire CAS technology) -- 8625

?2011 Texas Instruments Incorporated

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Roots Of Radical Equations

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Problem 1 ? Square Roots In this problem, students will graph the square root function. Students will then find the zeros of the equation--if there are any. Students may have to change the window to find the intersection points with the x-axis. Discussion Questions What are the characteristics of an equation that crossed

the x-axis? What are the characteristics of an equation that did not cross the x-axis? Why? What do you notice about graphs with a negative in front of the radical versus without a negative?

If using Mathprint OS: When entering the function in Y1 and students press y C, the cursor will move under the radical sign. Students should enter the value of the radicand and then press ~ to move out from under the radical sign.

Algebra 2

Problem 2 ? Cubic Roots

In this problem, students will graph the cubic root function. Students will then find the zeros of the equation--if there are any. Students may have to change the window to find the intersection points with the x-axis.

Discussion Questions

What are the characteristics of an equation that crossed the x-axis? What are the characteristics of an equation that did not cross the x-axis? Why?

What do you notice about graphs with a negative in front of the radical versus without a negative?

?2011 Texas Instruments Incorporated

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Roots Of Radical Equations

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