A study measuring the max height reached for various launch velocities and obtained the following data:

V at m/s max height
0 0
10 28
20 35
30 42
40 49
50 56
60 63
70 70

1. plot the data on a graph
2. draw a best-fit line or curve through the data points

To plot the data on a graph and draw a best-fit line or curve, you can follow these steps:

1. Set up a coordinate system: On a piece of graph paper or using graphing software, create a horizontal axis (x-axis) to represent the launch velocity (V) measured in m/s, and a vertical axis (y-axis) to represent the maximum height reached.

2. Plot the data points: On the graph, locate each data point from the given table of values and mark its corresponding coordinates. For example, plot the point (0, 0) for the first data pair, (10, 28) for the second data pair, and so on.

3. Connect the data points: Use a ruler or freehand to draw a line or curve that best connects the plotted data points. This line or curve represents the trend or relationship between the launch velocity (V) and the maximum height reached.

4. Determine whether a line or curve is appropriate: Look at the pattern formed by the plotted points. If the points seem to follow a straight-line pattern, a linear fit may be appropriate. If the points curve upwards or downwards, a non-linear curve fit might be more suitable.

5. Draw a best-fit line or curve: Depending on the pattern observed, draw a line or curve that approximately fits the general trend of the data. If using a linear fit, draw a straight line that best represents the general direction of the plotted points. If using a non-linear fit, draw a smooth curve that best approximates the pattern formed by the data.

6. Extend the line or curve: Extend the line or curve, if necessary, beyond the plotted data points to help visualize the trend or make predictions outside the given data range.

Note: If you are using graphing software, there are built-in tools and functions that can perform the regression analysis and draw the best-fit line or curve automatically.