0
One way to create one is to write it out with the point you want in factored form and then multiply it For example, let's say I want a polynomial with (3,0), (900,0) and (-4,0) I could write y=(x-3)(x-900)(x+4) and when I multiply this out I have a degree 3 poly. If i want a y other than zero, say I want y to be 100, then just add that to the right hand side.
What else can I help you with?
How do you graph a polynomial in order to solve for the Zeros?
Either graph the polynomial on graph paper manually or on a graphing calculator. If it is a "y=" polynomial, then the zeroes are the points or point where the polynomial touches the x-axis. If it is an "x=" polynomial, then the zeroes are the points or point where the polynomial touches the y-axis. If it touches neither, then it has no zeroes.
What is the answer an value of a polynomial is a value for which the polynomial is bigger than any other nearby values.?
The answer you're looking for is a "local maximum." A local maximum of a polynomial is a point where the polynomial's value is greater than the values of the polynomial at nearby points. Mathematically, this occurs when the first derivative is zero (indicating a critical point) and the second derivative is negative (indicating concavity). Local maxima can occur at one or more points within the polynomial's domain.
What is a polynomial function as a graph?
A polynomial function have a polynomial graph. ... That's not very helpful is it, but the most common formal definition of a function is that it is its graph. So, I can only describe it. A polynomial graph consists of "bumps", formally called local maxima and minima, and "inflection points", where concavity changes. What's more? They numbers and shape varies a lot for different polynomials. Usually, the poly with higher power will have more "bumps" and inflection points, but it is not a absolute trend. The best way to analyze the graph of a polynomial is through Calculus.
How do you graph a polynomial?
Basically the same way you graph most functions. You can calculate pairs of value - you express the polynomial as y = p(x), that is, the y-values are calculated on the basis of the x-values, you assign different values for "x", and calculate the corresponding values for "y". Then graph them. You can get more information about a polynomial if you know calculus. Calculus books sometimes have a chapter on graphing equations. For example: if you calculate the derivative of a polynomial and then calculate when this derivate is equal to zero, you will find the points at which the polynomial may have maximum or minimum values, and if you calculate the derivative at any point, you'll see whether the polynomial increases or decreases at that point (from left to right), depending on whether the derivative is positive or negative. Also, if you calculate when the second derivative is equal to zero, you'll find points at which the polynomial may change from convex to concave or vice-versa.
What is the minimum number of data points needed from which to identify a fractal with x y and z axes?
There can be no minimum number - it is simply not possible. Given any n points in 3-dimensional space, it is possible to find a polynomial that will generate a curve going through each of those points. There are other functions which will also do the trick. So, given any number of points, it would be impossible to determine whether they were generated by a fractal or a polynomial (or other function).
How do you graph a polynomial in order to solve for the Zeros?
Either graph the polynomial on graph paper manually or on a graphing calculator. If it is a "y=" polynomial, then the zeroes are the points or point where the polynomial touches the x-axis. If it is an "x=" polynomial, then the zeroes are the points or point where the polynomial touches the y-axis. If it touches neither, then it has no zeroes.
What do the zeros of a polynomial function represent on a graph?
The zeros of a polynomial represent the points at which the graph crosses (or touches) the x-axis.
What is the answer an value of a polynomial is a value for which the polynomial is bigger than any other nearby values.?
The answer you're looking for is a "local maximum." A local maximum of a polynomial is a point where the polynomial's value is greater than the values of the polynomial at nearby points. Mathematically, this occurs when the first derivative is zero (indicating a critical point) and the second derivative is negative (indicating concavity). Local maxima can occur at one or more points within the polynomial's domain.
What is the point at which a graph crosses the x-axis?
For a line, this is the x-intercept. For a polynomial, these points are the roots or solutions of the polynomial at which y=0.
How do you find the roots of a polynomial of graphed points?
Join the points using a smooth curve. If you have n points choose a polynomial of degree at most (n-1). You will always be able to find polynomials of degree n or higher that will fit but disregard them. The roots are the points at which the graph intersects the x-axis.
What is a polynomial function as a graph?
A polynomial function have a polynomial graph. ... That's not very helpful is it, but the most common formal definition of a function is that it is its graph. So, I can only describe it. A polynomial graph consists of "bumps", formally called local maxima and minima, and "inflection points", where concavity changes. What's more? They numbers and shape varies a lot for different polynomials. Usually, the poly with higher power will have more "bumps" and inflection points, but it is not a absolute trend. The best way to analyze the graph of a polynomial is through Calculus.
The graph of a polynomial changes direction twice and has only one root What can you say about the polynomial?
It is a polynomial of odd power - probably a cubic. It has only one real root and its other two roots are complex conjugates. It could be a polynomial of order 5, with two points of inflexion, or two pairs of complex conjugate roots. Or of order 7, etc.
How many extreme points does a degree of 4 have?
A polynomial of degree 4 can have up to 3 local maxima/minima.
Will any 4 coordinates on a graph produce a Cubic equation?
Four points can produce a polynomial of at most the third order - a cubic. It is, of course, possible that the 4 points are collinear.
How do you graph a polynomial?
Basically the same way you graph most functions. You can calculate pairs of value - you express the polynomial as y = p(x), that is, the y-values are calculated on the basis of the x-values, you assign different values for "x", and calculate the corresponding values for "y". Then graph them. You can get more information about a polynomial if you know calculus. Calculus books sometimes have a chapter on graphing equations. For example: if you calculate the derivative of a polynomial and then calculate when this derivate is equal to zero, you will find the points at which the polynomial may have maximum or minimum values, and if you calculate the derivative at any point, you'll see whether the polynomial increases or decreases at that point (from left to right), depending on whether the derivative is positive or negative. Also, if you calculate when the second derivative is equal to zero, you'll find points at which the polynomial may change from convex to concave or vice-versa.
How do you do a polynomial?
Basically the same way you graph most functions. You can calculate pairs of value - you express the polynomial as y = p(x), that is, the y-values are calculated on the basis of the x-values, you assign different values for "x", and calculate the corresponding values for "y". Then graph them. You can get more information about a polynomial if you know calculus. Calculus books sometimes have a chapter on graphing equations. For example: if you calculate the derivative of a polynomial and then calculate when this derivate is equal to zero, you will find the points at which the polynomial may have maximum or minimum values, and if you calculate the derivative at any point, you'll see whether the polynomial increases or decreases at that point (from left to right), depending on whether the derivative is positive or negative. Also, if you calculate when the second derivative is equal to zero, you'll find points at which the polynomial may change from convex to concave or vice-versa.
What is the minimum number of data points needed from which to identify a fractal with x y and z axes?
There can be no minimum number - it is simply not possible. Given any n points in 3-dimensional space, it is possible to find a polynomial that will generate a curve going through each of those points. There are other functions which will also do the trick. So, given any number of points, it would be impossible to determine whether they were generated by a fractal or a polynomial (or other function).
