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.
Still curious? Ask our experts.
Chat with our AI personalities
Rene
Beau
EzraAdd your answer:
Earn +20 pts
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 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).
What are the conditions for error to be minimum in least squares approximation?
Let's start with a first degree polynomial equation:This is a line with slope a. We know that a line will connect any two points. So, a first degree polynomial equation is an exact fit through any two points with distinct x coordinates.If we increase the order of the equation to a second degree polynomial, we get:This will exactly fit a simple curve to three points.If we increase the order of the equation to a third degree polynomial, we get:This will exactly fit four points.if we have more than n + 1 constraints (n being the degree of the polynomial), we can still run the polynomial curve through those constraints. An exact fit to all constraints is not certain (but might happen, for example, in the case of a first degree polynomial exactly fitting three collinear points). In general, however, some method is then needed to evaluate each approximation. The least squares method is one way to compare the deviations.
