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For a polynomial of order n there are n+1 coefficients that can be changed. There are therefore 2^(n+1) related polynomials with coefficients of the same absolute values. All these generate graphs whose shapes differ.

If only the constant coefficient is switched, the graph does not change shape but moves vertically. If every coefficient is switched then the graph is reflected in the horizontal axis. For all other sign changes, there are intermediate changes in the shape of the graph.

Q: How does changing the signs of the coefficients affect the graph of a polynomial?

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The degree is equal to the maximum number of times the graph can cross a horizontal line.

A value of the variable when the polynomial has a value of 0. Equivalently, the value of the variable when the graph of the polynomial intersects the variable axis (usually 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.

The order of the polynomial (the highest power) and the coefficient of the highest power.

A root is the value of the variable (usually, x) for which the polynomial is zero. Equivalently, a root is an x-value at which the graph crosses the x-axis.

Related questions

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.

The zeros of a polynomial represent the points at which the graph crosses (or touches) the x-axis.

false

Not quite. The polynomial's linear factors are related - not equal to - the places where the graph meets the x-axis. For example, the polynomial x2 - 5x + 6, in factored form, is (x - 2) (x - 3). In this case, +2 and +3 are "zeroes" of the polynomial, i.e., the graph crosses the x-axis. That is, in an x-y graph, y = 0.

no

A parabola.

The graph of a polynomial in X crosses the X-axis at x-intercepts known as the roots of the polynomial, the values of x that solve the equation.(polynomial in X) = 0 or otherwise y=0

Changing the constant in a function will shift the graph vertically but will not change the shape of the graph. For example, in a linear function, changing the constant term will only move the line up or down. In a quadratic function, changing the constant term will shift the parabola up or down.

The zero of a polynomial in the variable x, is a value of x for which the polynomial is zero. It is a value where the graph of the polynomial intersects the x-axis.

What is the interpretation of a graph quadratic polynomial

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.

B