10 Academic Date: Enter this equation into in DESMOS. Adjust your screen to show the scales like they are shown in the grid below.
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1 Academic Date: Open: DESMOS Graphing Calculator Task : Let s Review Linear Relationships Bill Bob s dog is out for a walk. The equation to model its distance awa from the house, d metres, after t seconds is: d.t 5. Enter this equation into in DESMOS. Adjust our screen to show the scales like the are shown in the grid below.. Complete the Distance column in the table below. To calculate the distances, ou can: You can use the equation above and our calculator. You can use the TRACE feature on the online graphing calculator. Time Distance Finite Differences (sec) (m) First Differences 4 5. Graph the relation on the grid.. a. How far from the house is the dog when he starts his walk? This is the -intercept. Please label this point on the graph. b. At what rate does the dog walk? This is the slope. Please indicate this on the graph with a rate triangle. 4. Calculate the first differences? Do ou remember how? 5. The first differences are all equal. What does that tell ou about the relationship between d and t? Page of 5
2 Academic Date: Task : Quadratic Relations Now, let s kick it up a notch!!! Bill Bob s dog is now going to run, fetch a frisbee, and then run back. The equation to model the distance, d metres, the dog is awa from Bill Bob after t seconds is: d.5t.5t. Enter this equation in the online graphing calculator. 6. Complete the Height column in the table below. To calculate the height, ou can: You can use the equation above and our calculator. You can use the TRACE feature on the online graphing calculator. Time (s) Height (m) Finite Differences First Second Differences Differences Graph the relation on the grid. 8. a. How far is the dog from Bill Bob when he starts running? This is the -intercept. b. What is the maimum distance between the dog and Bill Bob? This is the verte. c. This shape is called a parabola. Draw a vertical line through the verte of the parabola. This is the ais of smmetr. d. Would ou sa that this parabola opens up or opens down? e. When is the dog m awa from Bill Bob? These are the zeros! (aka: -intercepts). 9. On the graph, label and calculate the following: a. -intercept b. verte c. ais of smmetr d. zeros. Calculate the first differences.. The first differences are not equal. What does that tell ou about the relationship between d and t?. Calculate the second differences. You do this b calculating the first differences of the first differences.. The. This means that the relationship is. 4. How does the equation of a Linear Relation compare to the equation of a Quadratic Relation? Page of 5
3 graph direction degree equations shape general equation Academic Date: Linear Quadratic slope/-intercept: slope/point: standard: standard: verte: - - finite diff. st Diff. - - st Diff. nd Diff. first differences are if first differences are + = if first differences are - = first differences are second differences are if second differences are + = if second differences are - = Page of 5
4 eample ke properties Academic Date: -intercept: -intercept: zeros (-intercepts): slope: verte: direction of opening: ma/min ais of smmetr: finite diff. st Diff. - - st Diff. nd Diff. slope = -intercept = -intercept = zeros (-intercepts) = verte = ma/min = direction of opening = ais of smmetr = Page 4 of 5
5 Academic Date: Eamples: A B C the verte the -intercept the zeros state the equation & draw in the ais of smmetr does the parabola open up or down? is the verte a ma or a min? finite differences Page 5 of 5
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