4Graphing Navigation… Typing Equations Always set your equation equal to zeroUse the correct syntax (see Basic Computations)Turn off Plots2nd, STAT PLOT, 4:Plots Off, ENTER
5Graphing Navigation… Viewing Window To display x:[-10, 10]; y:[-10, 10]* ZOOM 6: StandardTo show all points on a scatter plot* ZOOM 9: StatTo show entire graph on the screen* ZOOM 0: FitTo 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
6Graphing Navigation… Viewing Window Example: * Graph x3 – 1.1x2 – 65.4x = – 229.5x:[4.95, 5.15]; 0.05y:[–0.1, 0.1]; 0.01Does the graph have any zeros?
7Graphing Tools… Calculating Extrema (minimum/maximum) 2nd, CALC 3:minimum or 4: maximumLB, ENTER, RB, ENTER, Guess?, ENTERx = (where it occurs)y = min/max value
11Statistics and Algebraic Models… Scatter Plots* Plotting PointsClear Y=Turn on Plot 1: 2nd, STAT PLOT, 1, ON, ENTEREnter ordered pairs: STAT – 1:EditEnter x-coordinates for L1Enter y-coordinates for L2ZoomStat to view graph
12Statistics and Algebraic Models Lines of Best FitSTAT – CALCChoose type of equation:4: Line5: Quadratic6: Cubic7: QuarticType 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: Y1Press ENTERThe algebraic model is shown on the graph, and the equation is located in Y1
13Example: * Make a scatter plot of the data: * Find a linear model, quadratic model, cubic modelLinear Equation: y = 0.572xQuadratic Equation: y = 0.059x2 – 0.617xCubic Equation:y = –0.0124x x2 – 3.269xx5101520y10.12.88.116.017.8
14Life Expectancy (years) Make a 2 scatter plots of the data:* Men: Plot 1* Women: Plot 2* set x = 0to representthe 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 BirthMenWomen197067.174.7198070.077.4199071.878.8200073.280.2201074.581.3
15Find 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?