Graphing Navigation… Typing Equations –Always set your equation equal to zero –Use the correct syntax (see Basic Computations) –Turn off Plots 2 nd, STAT PLOT, 4:Plots Off, ENTER
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
Graphing Navigation… Viewing Window Example: * Graphx 3 – 1.1x 2 – 65.4x = – x:[4.95, 5.15]; 0.05 y:[–0.1, 0.1]; 0.01 Does the graph have any zeros?
Graphing Tools… Calculating Extrema (minimum/maximum) 2 nd, CALC 3:minimum or 4: maximum LB, ENTER, RB, ENTER, Guess?, ENTER x = (where it occurs) y = min/max value
Graphing Tools… Finding Zeros/Roots (x-intercepts, solutions) 2 nd, CALC 2: zero LB, ENTER, RB, ENTER, Guess?, ENTER x = (where it occurs) y = 0
Graphing Tools Locating Points of Intersection (two graphs) 2 nd, CALC 5: intersect 1 st curve, ENTER, 2 nd curve, ENTER, Guess?, ENTER
Statistics and Algebraic Models… Scatter Plots * Plotting Points Clear Y= Turn on Plot 1: 2 nd, 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
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, Y 1 -Use the 2nd button to type L1 and L2 -Dont forget the comma -To find Y1 press VARS, Y-VARS, 1:Function, 1: Y 1 Press ENTER The algebraic model is shown on the graph, and the equation is located in Y 1
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 x 2 – 3.269x x y
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 MenWomen
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. a.Find a linear model, a quadratic model, a cubic model, and a quartic model for the data. Let x = 0 represent b.Graph each model. Which one is the better fit? c.Use each model to determine the current energy production. Which model has the most reasonable answer?