# Graphing Question

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Is there a "rule" or something to tell when you should graph something as a straight line vs when it should be a...I don't know what to call it...half of a parabola? For ex, when graphing a speed (time/distance) problem, will the result always be a half-parabola? TIA!

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yes, there is a "rule".

A straight line corresponds to a LINEAR relationship.

A parabola corresponds to a QUADRATIC relationship.

I do not know what you mean by "graphing a speed".

The position vs time graph will be a straight line if the speed is constant, because the velocity is the slope of the position-vs-time graph, and a constant slope means a straight line.

The position vs time graph will be parabolic if the velocity, i.e. the slope of the x-t-curve, changes linearly with time; this is the case if there is a constant acceleration.

Rather than memorizing how to graph "speed", the student needs to analyze the relationship between the two quantities that he graphs.

There are also plenty of relationships between two quantities that result neither in a linear nor in a parabolic graph.

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The simple answer is that linear functions (equations with just x) are straight lines. If x is raised to a power or in a log, then the graph will change and begin doing various other things. That is by no means all of the information, merely an extremely simplified answer.

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Thanks! I suspected that it had something to do w/ linear equations vs. ??? The set of questions ds was dealing with were more theoretical than solve an actual equation, so I figured there had to be a rule of thumb, but I couldn't figure out how to phrase the question for Google.

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Ok, sorry--after reading the linked site, I'm still not sure I understand well enough.

The question in the math book is: "The distance required to stop your car depends on how fast you are going when you apply the brakes." The student is supposed to sketch a "reasonable" graph. Ds sketched a straight line; the book has the shape that belongs more to a "power function."

He made this mistake on several of the Reasonable Graph problems (I hate the ones that don't have more definitive answers!), so I figured there was a...Reason of some sort.

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The question in the math book is: "The distance required to stop your car depends on how fast you are going when you apply the brakes." The student is supposed to sketch a "reasonable" graph. Ds sketched a straight line; the book has the shape that belongs more to a "power function."

He made this mistake on several of the Reasonable Graph problems (I hate the ones that don't have more definitive answers!), so I figured there was a...Reason of some sort.

To correctly graph this, the student would need a knowledge of physics.

IF (and only if!) the driver brakes so that the deceleration is constant, i.e. the velocity decreases with time at a constant rate, the relationship between stopping distance and velocity is a quadratic one.

The distance d for the car to come to a stop is given by the equation d= V^2/(2a), where v is the speed of the car when the driver begins to brake, and a is the absolute value of the acceleration, the rate at which the speed changes.

For a student who does NOT know physics or who is not given this relationship, it makes absolutely no sense to ask this question!

If your DS has not had physics or was not given the equation, he has no way of knowing that the distance does not increase linearly with v, but rather quadratic.

As long as his guess is that the greater the speed, the greater the distance, he has answered the question correctly and has not made a mistake.

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Normally questions like this in graphing chapters are wanting your son to see that when you put on the brakes, the car's speed decreases. It does not immediately jump from 60 to 30, nor does it stay constant. It slowly slopes downward at a non-constant rate. If the car comes to a complete stop, it goes to zero. If the car slows then increases its speed higher than it was previously traveling then the picture has a big V in it where the right side is higher. It is asking your son to recognize what the graph is telling him or for him to be able to give a quick version of what life looks like in graphic form.

If he is having trouble, then you might want him to physically move his finger along the graph talking to you about what is happening. Have him go through a simple action explaining what is happening.

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