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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?
In given figure graph of polynomial x is given find the zero of polynomial?
To find the zeros of the polynomial from the given graph, identify the points where the graph intersects the x-axis. These intersection points represent the values of x for which the polynomial equals zero. If the graph crosses the x-axis at specific points, those x-values are the zeros of the polynomial. If the graph merely touches the x-axis without crossing, those points indicate repeated zeros.
What is a cubic polynomial of this degree?
A cubic polynomial is a polynomial of degree three, which means its highest exponent is three. It takes the general form ( ax^3 + bx^2 + cx + d ), where ( a, b, c, ) and ( d ) are constants, and ( a \neq 0 ). The graph of a cubic polynomial can have one or two inflection points and can exhibit a variety of shapes, including one or two turning points.
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.
How many extrema can a 8th polynomial have?
An 8th degree polynomial can have up to 7 extrema (local maxima and minima). This is because the number of extrema is limited by the degree of the polynomial minus one, which in this case is (8 - 1 = 7). However, the actual number of extrema can be fewer depending on the specific polynomial and its critical points.
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.
In given figure graph of polynomial x is given find the zero of polynomial?
To find the zeros of the polynomial from the given graph, identify the points where the graph intersects the x-axis. These intersection points represent the values of x for which the polynomial equals zero. If the graph crosses the x-axis at specific points, those x-values are the zeros of the polynomial. If the graph merely touches the x-axis without crossing, those points indicate repeated zeros.
What is a cubic polynomial of this degree?
A cubic polynomial is a polynomial of degree three, which means its highest exponent is three. It takes the general form ( ax^3 + bx^2 + cx + d ), where ( a, b, c, ) and ( d ) are constants, and ( a \neq 0 ). The graph of a cubic polynomial can have one or two inflection points and can exhibit a variety of shapes, including one or two turning points.
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.
How many extrema can a 8th polynomial have?
An 8th degree polynomial can have up to 7 extrema (local maxima and minima). This is because the number of extrema is limited by the degree of the polynomial minus one, which in this case is (8 - 1 = 7). However, the actual number of extrema can be fewer depending on the specific polynomial and its critical points.
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.
Can a fourth degree polynomial touch the x axis three times?
No, a fourth degree polynomial cannot touch the x-axis three times. A polynomial can touch the x-axis at an even number of points, which corresponds to the multiplicity of its roots. If it touches the x-axis at three points, one of those points would have to be of odd multiplicity, which would make the total multiplicity odd, contradicting the fact that a fourth degree polynomial has an even degree. Thus, it can touch the x-axis at either 0, 2, or 4 points.
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 make a graph with polynomials with three hills?
To create a graph of a polynomial with three hills, you'll want a polynomial function that has three local maxima. A simple way to achieve this is to use a polynomial of degree 5 or higher, such as ( f(x) = x^5 - 15x^3 + 20x ), which has the necessary critical points. Use calculus to find the derivative, set it to zero, and solve for critical points to ensure there are three maxima. Finally, plot the function, ensuring it has the desired number of hills (peaks) between the x-intercepts.
What is polynomial spline?
A polynomial spline is a piecewise-defined polynomial function used to create smooth curves that pass through or near a set of data points. It is constructed by connecting multiple polynomial segments, each defined on an interval, ensuring that these segments are continuous and have continuous derivatives up to a specified order at their junctions (knots). This flexibility allows polynomial splines to effectively model complex shapes and relationships in data. Common types include linear, quadratic, and cubic splines, with cubic splines being particularly popular for their smoothness and simplicity.
