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What is a root in a polynomial graph?
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.
How do the zeros of a polynomial function help you determine the answer?
They tell you where the graph of the polynomial crosses the x-axis.Now, taking the derivative of the polynomial and setting that answer to zero tells you where the localized maximum and minimum values occur. Two values that have vast applications in almost any profession that uses statistics.
What can the degree of a polynomial tell you about the graph?
The degree is equal to the maximum number of times the graph can cross a horizontal line.
What best describes a root of a polynomial?
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).
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.
Can the graph of a polynomial function have a vertical asymptote?
no
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.
how many roots does the graphed polynomial function have?
here is the graph
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.
What is the definition for the zero of a polynomial function?
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 does it mean to be a root of a polynomial?
A root of a polynomial is a value of the variable for which the polynomial evaluates to zero. In other words, if ( p(x) ) is a polynomial, then a number ( r ) is a root if ( p(r) = 0 ). Roots can be real or complex and are critical for understanding the behavior and graph of the polynomial function. The Fundamental Theorem of Algebra states that a polynomial of degree ( n ) has exactly ( n ) roots, counting multiplicities.
What is the test that determines if a graph is a function?
The vertical line test determines if a graph represents a function. If a vertical line intersects the graph at more than one point, the graph does not represent a function, as this indicates that a single input (x-value) corresponds to multiple outputs (y-values). Conversely, if every vertical line intersects the graph at most once, it confirms that the graph is a function.
How do you do a parabola?
A parabola is a graph of a 2nd degree polynomial function. Two graph a parabola, you must factor the polynomial equation and solve for the roots and the vertex. If factoring doesn't work, use the quadratic equation.
What is a root in a polynomial graph?
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.
Use a graphing utility to graph the sine function and its polynomial approximation in the sme viewing window?
Yes, I did.
What is the name of graph of a cubic polynomial?
The graph of a cubic polynomial is called a cubic curve. It typically has an "S" shape and can have one, two, or three real roots, depending on the polynomial's coefficients. The general form of a cubic polynomial is ( f(x) = ax^3 + bx^2 + cx + d ), where ( a \neq 0 ). The behavior of the graph includes turning points and can exhibit inflection points where the curvature changes.
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.
