find the constant difference for each of the tables below. use these results to determine if each table represents a linear, quadratic, or a cubic function. then find the equation of each function.

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silvernight269 · Answer

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silvernight269 · Answer

@dude

dude · Answer

Sorry for the late response

First find the slope for the first table

Chose any 2 points (preferably ones next to each other)
 
Say for example you choose (-13,41) and (-7,23)
                                            (  x$_1$,$y_1$)         (x$_2$, $y_2$)

Use the equation to find slope
$\large\frac{y_2-y_1}{x_2-x_1}=\frac{23-41}{-7-(-13)}$ 
Once you do that choose another two points

Lets say you choose (-7,23) and (-1,5)
                               ( x$_1$,$y_1$)      (x$_2$, $y_2$)

And use the same equation

$\large\frac{y_2-y_1}{x_2-x_1}=\frac{5-23}{-1-(-7)}$

If they are the same, then it is a linear function (they have the same slope)

dude · Answer

From them you can just use any point (from the table) and substitute what you have to find the y-intercept

dude · Answer

For the second table we can clearly see that they are not going on a constant rate

In terms of it being a quadratic function, the points would be the same on both positive and negative values after it reaches its vertex

dude · Answer

So it is automatically a cubic function (I am not sure how to fully explain this however here is the graph and so I hope it does help, will try to explain though) https://www.desmos.com/calculator/uu5ygqwf24

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