What Is the Maximum Number of Times a Line Can Cross the X-axis?
Equations and Graphs
Overview: In this module we review the essentials of interpreting and preparing graphical data and revisit the graphical add-on of vectors.
Skills:
- Determining slopes and y-intercepts from graphs
- Estimating specific data values from graphs
In the sciences, many times it is necessary to be able to interpret graphs as well every bit be able to graph certain equations. Oft data is bachelor in a graphical format and y'all must be able to extract the necessary information. Other times, it may be helpful to plot an equation in guild to fully understand a problem. Nonetheless, graphing can be difficult for some students. The format in this section is a little unlike. The first part will be simply showing what some special equations look like in graphical course and the second part will be a series of questions to assist you lot understand graphs better.
 | This graph shows a straight line and the corresponding equation is y = mx + b. Y is the y value (altitude along the y-axis, which is the vertical axis) and 10 is the x value (the distance along the ten-axis, which is the horizontal centrality). The slope of the line is m, which is likewise the rise/run or the D10/Dy. The y-intercept of the line is b. This is the y value where the line crosses the y-axis (when the 10 = 0). In the graph here, the gradient is 1 and b is +two. Notice that a line crosses each axis only once (at most). |
 | This graph represents a quadratic function, which is y = ax2 + bx + c. The parameters a, b and c are constants. In this graph the actual equation is y = 2x2 + 3x - 2. Notice that in this graph the function crosses the y-axis in one case and the ten-centrality twice. This has to practice with the fact that x is squared in the equation and y is non. The function crosses the centrality (upward to) the same number of times equally the power of that value. In this graph ten is squared so the line crosses the x-axis up to two times. |
 | This graph shows a cubic equation, which is expressed mathematically every bit y = axiii + bx2 + cx + d. For this item part, y = ten3 + 2 ten2 - ii 10 - 3. Because x is raised to the third power, the function crosses the x-axis 3 times. It crosses the y-axis only in one case however. |
 | This is a log plot. Discover that the ten-axis is quite different than in the other graphs. In this graph, if we expect at the y-centrality nosotros encounter that the distance from i to 10 is the aforementioned every bit that from 10 to 100. But nosotros know that the span from x to 100 represents a much larger range of 10-values than that from 1 to 10. This is a property of a log plot. Be sure to look at the axis on a log plot (besides as all graphs) in lodge to sympathise exactly what the graph is trying to show. |
In order to reply the following questions, you demand to have a good understanding of the preceding subjects in the tutorial.
| one. | A particle'south move is plotted on the right. Apply the information to answer the post-obit questions.
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| 2. | Some other particle moves on a trajectory described in the plot on the right.
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| 3. | A brawl is dropped from the top of a edifice and its fall is plotted in the graph to the right.
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Summary
In this module we have reviewed the essential skills necessary for interpreting data presented in a graphical format. Interpretation of graphical data is a routine skill used past the practicing scientists, physicians, and engineers. You volition develop these skills further in your specific discipline at Washington Univeristy.Return to the Chemistry Subject Alphabetize
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Source: http://chp090.chemistry.wustl.edu/~coursedev/Online%20tutorials/Eqns.htm
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