Learning how to solve quartic polynomials, which are polynomials in degrees of four in
the form of f(x)=ax^4+bx^3+cx^2+dx+e, is not a very hard thing to do. It just takes a little time
and dedication as well as knowledge about things such as end behavior, local extrema, zeros,
Descartes rule of sign, intermediate value theorem, rational zero theorem, remainder theorem,
remaining zeros and multiplicity and intercepts to understand the quartic polynomial even more.
In this paper, all of the items above will be mentioned and thoroughly talked about as we analyze
the quartic polynomial f(x)=6x⁴+11x³-16x²-11x+10.
One of the first things we will look at is the end behavior of the quartic polynomial. End
behavior is how the starting and the ending point of a function approach infinity. It is called end
…show more content…
To find end behavior with
a calculator, plug the function into the y= button. Next click on the graph button and view your
quartic polynomial. If you cannot see it you may have to zoom out by pressing the zoom button
and going down to 0:Best Fit. While viewing your graph, you must pay close attention to what
the start and the end functions are doing. If the left end is coming from the bottom, then the end
behavior for that end would be as x approaches negative infinity or x→-∞ (it would be negative
infinity because it is on the left or negative side), f(x) approaches negative infinity or f(x)→-∞.
This is because it is coming from the bottom where the numbers are negative and if the line
where to keep going, it would continue down until it reached negative infinity. If the left side end
were coming from the top, the end behavior would be as x approaches negative infinity or x→-
∞, f(x) approaches positive infinity because it came from the top where the numbers are
For my derivative project I chose to graph Emmitt Smith’s annual rushing yard total. Emmitt was drafted out of University Florida in 1990 and began his career as an NFL Great. As you can see on the graph, Smith began his career slowly, amassing only 937 rushing yards his rookie year. However, his second year Smith improved to 1563 rushing yards. In his third season, Smith again improved to 1713 rushing yards. The decrease in production Smith’s fourth and fifth year (1486 and 1494 respectively) in the NFL can be partially credited to the fact Smith did not compete in all sixteen regular season games due to injuries. Smith redeemed himself the following year with a career high 1773 rushing yards. Over the next six years Smith’s age slowly caught up to him as he ranged from 1021 to 1397 yards. Finally, after his thirteenth year as a Dallas Cowboy, Smith was traded to the Arizona Cardinals. In his first year with the Arizona Cardinals (2003), Smith was injured and played as a backup for the majority of the year. This is illustrated through his career low 256 rushing yards. However, in Smith’s final year in the NFL, he rushed for 937 rushing yards, bouncing back from a disappointing year. Strangely, Smith ended his last season with the same rushing total as his rookie season. I plotted these points in a graph in an excel document and created a line of best fit. This line was a cubic equation (f(x) = 1.4228x3 - 8533.3x2 + 2E+07x - 1E+10).
1.) With the two-point threshold as a task, how would you demonstrate the method of limits?
acid. The volume is different because of the different pH. The phase here changes from acidic to
* "There is an end to the rainbow." -- This is not true. A rainbow is relative to the observers position. Because of this, as an observer moves, so does the rainbow. This means that the "end" moves as well, and can never be found. Also once the sun has disappeared or the observer turns to face the sun, the rainbow disappears.
from beginning to end and this can be said to be the first level of
Termination condition is the condition that ends the evolutionary computation cycles. Termination condition can be the maximum number of cycles allowed, ore in case we know the optimal solution the value of that solution.
To further this investigation, one could look into a formula that works for negative indices and compare this to positive integer formula. A pattern could be found from the two results and a formula could be created that works and generates answers for both positive and negative indices.
never reach the end of the course, as it would be infinitely long, much as the
the root to the function, like if it is a parabola with its vertex is placed
will be able to draw a graph of my results and then use this to work
if we carry on this way, such as The ending of The Machine Stops when
view, the ends of things are seen as providing the meaning for all that has
to 10 along the x axis and from 0 to 100 on the y axis. The curve will
The beginning of a thing is its birth. The end of that thing is its death. Within the broad framework of our lives--the coordinate system that begins at age zero and completes some sort of cycle when our bodies stop breathing--we experience an infinite number of