1
vote
0answers
23 views

Quartic Polynomial Manipulation

I have a quartic polynomial in $x$ (too long to write here) $f(x,c_1, c_2, c_2)$ where $c_1, c_2, c_3$ are constants which I have complete freedom over how to fix their values, as long as they are ...
-2
votes
3answers
30 views

Graphing polynomial functions

I am having problems understanding how to graph $(x^2 -1)(x^2 -9)$, Any help would be much appreciated! Thanks
0
votes
5answers
69 views

Graphing polynomials

Sketch a graph of the polynomial $P(x)=(x-2)^2(x+1)^3$. You must plot and label the x and y intercepts and these should be the only points you plot. How do I sketch the graph of a polynomial?
2
votes
2answers
46 views

Problem with powers

I hope this has not been asked already. while reading a material on upper bounds of polynomials (time complexity) they compared growth of various polynomial functions (like $N\log N$, $N^2$, $N^3$, ...
0
votes
1answer
27 views

Seeing complex roots on the graph of a polynomial

When I sketch the graph for a general second degree polynomial $y = ax^2 + bx + c$ it is easy to "see" its roots by looking at the points where $y=0$. This is true also for any $n$-degree polynomial. ...
0
votes
2answers
103 views

Curve Fitting a Cyclical Pattern of Data

I'm analyzing phonological characteristics of the 22 letters used in the Hebrew alphabet, and assigned each letter an enumeration to see if they are organized based on place of articulation: ...
0
votes
1answer
365 views

Graphing: Given two points on a graph, find the logarithmic function that passes through both.

Is there such a method to do this? I would like to come up with a logarithmic function (a graph that looks like a square root graph) that passes through two given points. Haven't had any luck in ...
0
votes
1answer
54 views

Finding intersection points of 2 functions. My method is incomplete.

These are the 2 functions : $y = x^{4}-2x^{2}+1$ $y = 1-x^{2} $ Here's how I solved It : $x^{4}-2x^{2}+1 = 1-x^{2}$ $x^{4}-x^{2} = 0$ $x^2(x^2-1)=0$ $x^2-1=0$ $x=\pm \sqrt{1} $ Value of $y$ when ...
1
vote
5answers
96 views

If the leading coefficient of a polynomial is $x^{3}$, does it mean that the graph would always intersect the $x$ axis at $3$ points?

I had learnt that this was the case. Or is it not like that? Does the power of a polynomial indicate the number of times the graph cuts at the x axis?
0
votes
1answer
43 views

Sketching fuctions - standard meaning of terms?

When sketching the graphs of polynomials, do certain terms always have the same meaning? For example, in $f(x) = x^n + c$, the intersection with the y-axis is always $c$, no matter how high the ...
0
votes
2answers
82 views

What is the simplest $\Bbb{R}\to\Bbb{R}$ function with two peaks and a valley?

What is the simplest $\Bbb{R}\to\Bbb{R}$ function with two peaks and a valley? I have a set of points in $\Bbb{R^2}$ and I would like to fit a curve to the points, the points approximately lie on a ...
1
vote
1answer
338 views

Sketching a Cubic Polynomial?

Suppose that $f(x)$ has $(x-2)^2$ and $(x+1)$ as its only factors. How do I sketch the graph of $f$? So far what I've done is determine (hopefully correctly) that the x-intercepts will be at $-1$ and ...
-3
votes
2answers
879 views

How to Sketch a Quartic Polynomial??

Suppose that $f$ is a quartic polynomial with zeros at $-2,1,3,4$, and that $f(0)=4$. a. How can we sketch a graph of $f$? b. Then, if $f(x)$ is written in the form $f(x)=A(x-a)(x-b)(x-c)(x-d)$ ...
0
votes
4answers
161 views

How to graph the equation: $y=\frac {x-2}{x+1}$?

the title says it all. I'm pretty sure this is a hyperbola, but is there an alternative way of doing this besides a table of values? "Graph the equation $y=\frac {x-2}{x+1}$" I know that $x$ cannot ...
2
votes
3answers
141 views

How can complex polynomials be represented?

I know that real polynomials (polynomials with real coefficients) are sometimes graphed on a 3D complex space ($x=a, y=b, z=f(a+bi)$), but how are polynomials like $(1+2i)x^2+(3+4i)x+7$ represented?
2
votes
1answer
252 views

Plotting $(x^2 + y^2 - 1)^3 - x^2 y^3 = 0$

I have no idea how this equation: \begin{equation} (x^2 + y^2 - 1)^3 - x^2 y^3 = 0 \end{equation} Produces this picture: Can someone provide a general explanation of plotting this function?
0
votes
3answers
53 views

Determining a polynomial from its crossings with another polynomial

Is it possible to determine the coefficients of two polynomials, if we are given 2n different points at which they cross each other ? In other words, If $f(p) = \sum_{i}\alpha_{i}p^{i}$ and $g(p) = ...
0
votes
2answers
174 views

Power functions and parabola issue

With the function f(x)=x^2 we get a graph like so... The rule for power functions, that I've been told, is the larger the power gets, the closer the line will touch the x-axis. Example for ...
2
votes
2answers
2k views

Construct a polynomial function with the given graph

Where does one begin? I can see that the zeros are -5, -3, 0, and 4? Is that correct so far?
0
votes
1answer
10k views

How to use polyfit() function in Matlab?

First of all i am new to Matlab, and not sure whether to use polyfit or something else for my problem. I plotted a graph with the following matlab code: ...
1
vote
2answers
2k views

Graphing Cubic Functions

I'm having a Little bit of trouble in Cubic Functions, especially when i need to graph the Turning Point, Y-intercepts, X-intercepts etc. My class teacher had told us to use Gradient Method: lets ...
0
votes
2answers
81 views

Graphing a line of an expected value

Given E[x]=3, var[x]=9, Graph the line y=(x-1)(x-2)(x-3). How does one graph such a thing?
1
vote
2answers
656 views

How to find the equation for a graph of a polynomial function?

Consider this graph of a polynomial function. The correct equation is: $f(x) = x^3 - 3x$ Strictly speaking I don't know the equation and have to find it. So far I've done this: Degrees of the ...
2
votes
2answers
3k views

Find 5th degree polynomial equation from points?

I have a set of estimated points, listed below, and I would like to know how to calculate the polynomial. I've looked at Wikipedia, and I don't quite understand how at works. Example 1 on ...
2
votes
3answers
324 views

Do all polynomials of even degree start by decreasing as you plot from $-\infty$ upward?

Polynomials of degree 2, if the first term is positive, starts descreasing. Polynomials of degree 3, if the first term is positive, starts increasing. is this constant? like.. Polynomials of ...