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**TI-84 Graphing Calculator**

Basic Computations Graphing Navigation Graphing Tools Statistics and Algebraic Models

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**First… Clear Memory Degree Mode 2nd, MEM, Reset: all RAM, ENTER**

MODE, Degree, ENTER, 2nd, QUIT

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Basic Computations Example: Answer: Looks Like:

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**Graphing Navigation… Typing Equations**

Always set your equation equal to zero Use the correct syntax (see Basic Computations) Turn off Plots 2nd, STAT PLOT, 4:Plots Off, ENTER

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**Graphing Navigation… Viewing Window**

To display x:[-10, 10]; y:[-10, 10] * ZOOM 6: Standard To show all points on a scatter plot * ZOOM 9: Stat To show entire graph on the screen * ZOOM 0: Fit To zoom in/out from the center of the screen * ZOOM 2: Zoom In * ZOOM 3: Zoom Out * Best option…learn to use the WINDOW to manually edit the length of the x-axis and y-axis

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**Graphing Navigation… Viewing Window Example:**

* Graph x3 – 1.1x2 – 65.4x = – 229.5 x:[4.95, 5.15]; 0.05 y:[–0.1, 0.1]; 0.01 Does the graph have any zeros?

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**Graphing Tools… Calculating Extrema (minimum/maximum) 2nd, CALC**

3:minimum or 4: maximum LB, ENTER, RB, ENTER, Guess?, ENTER x = (where it occurs) y = min/max value

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**Graphing Tools… Finding Zeros/Roots (x-intercepts, solutions)**

2nd, CALC 2: zero LB, ENTER, RB, ENTER, Guess?, ENTER x = (where it occurs) y = 0

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**Graphing Tools Locating Points of Intersection (two graphs) 2nd, CALC**

1st curve, ENTER, 2nd curve, ENTER, Guess?, ENTER

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**Practice: x4 – 7x2 + 6x * zeros: –3, 0, 1, 2 * max: (0.456, 1.323)**

* Find the zeros, maximum, and minimums: x4 – 7x2 + 6x * zeros: –3, 0, 1, 2 * max: (0.456, 1.323) * min: (–2.056, –24.057) * min: (1.601, –1.766) x3 – 4x2 – 7x + 10 * zeros: –2, 1, 5 * max: (–0.694, ) * min: (3.361, –20.745) 10x x2 – 54.85x * zeros: -3, 1.1, * max: (–1.625, ) * min: (1.125, –0.026)

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**Statistics and Algebraic Models…**

Scatter Plots * Plotting Points Clear Y= Turn on Plot 1: 2nd, STAT PLOT, 1, ON, ENTER Enter ordered pairs: STAT – 1:Edit Enter x-coordinates for L1 Enter y-coordinates for L2 ZoomStat to view graph

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**Statistics and Algebraic Models**

Lines of Best Fit STAT – CALC Choose type of equation: 4: Line 5: Quadratic 6: Cubic 7: Quartic Type L1, L2, Y1 -Use the 2nd button to type L1 and L2 -Don’t forget the comma -To find Y1 press VARS, Y-VARS, 1:Function, 1: Y1 Press ENTER The algebraic model is shown on the graph, and the equation is located in Y1

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**Example: * Make a scatter plot of the data:**

* Find a linear model, quadratic model, cubic model Linear Equation: y = 0.572x Quadratic Equation: y = 0.059x2 – 0.617x Cubic Equation: y = –0.0124x x2 – 3.269x x 5 10 15 20 y 10.1 2.8 8.1 16.0 17.8

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**Life Expectancy (years)**

Make a 2 scatter plots of the data: * Men: Plot 1 * Women: Plot 2 * set x = 0 to represent the year 1970 * Find a quadratic model and cubic model for the data * Which model best fits the data? * What is the life expectancy for men & women in 2020? Life Expectancy (years) Year of Birth Men Women 1970 67.1 74.7 1980 70.0 77.4 1990 71.8 78.8 2000 73.2 80.2 2010 74.5 81.3

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**Find the minimum, maximum, and zeros of each function. **

Then find the point(s) of intersection of the functions. The table shows U.S. energy production for a number of years. Find a linear model, a quadratic model, a cubic model, and a quartic model for the data. Let x = 0 represent 1960. Graph each model. Which one is the better fit? Use each model to determine the current energy production. Which model has the most reasonable answer?

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