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False!

If the graph is exactly the same, then the x-intercepts will be the same which implies the roots are them same.

However, you can have the same roots and different graphs. So while the first statement is true, the converse if not.

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false

Q: Can polynomials with the same graph have different roots?

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The graph of a system of equations with the same slope will have no solution, unless they have the same y intercept, which would give them infinitely many solutions. Different slopes means that there is one solution.

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.

If you mean: y = 0.5x-10 then an equation parallel to it will have the same slope of 0.5 but a y intercept different to -10

A graph can be more useful for making presentations because it is more visual, and it can be easier to recognize a pattern in a graph for the same reason. However, a graph doesn't have any more data than a table with the same data.

no, coordinate graph is a graph made on a coordinate plane i.e xy-plane

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false

You keep them the same if they have different bases

Other polynomials of the same, or lower, order.

If you only look at the value of the roots and not their multiplicity then the answer is yes.The straight line y = x - 1 and the parabola y = (x - 1)^2 have the same root: x = 1. But the graphs are obviously different. All polynomials of the form y = (x - 1)^n will have x = 1 as the only root but they will have different shapes. The reason to this is that in the case of the straight line it is a root of multiplicity 1, in the case of a parabola it is a root of multiplicity 2 and in the case of y = (x - 1)^n it is a root of multiplicity n.

No.

theres nothing different because it is the same

The homonym of "routes" is "roots." They sound the same but have different meanings.

No! Bar and line graphs are different bar graphs show bars and line graph shows lines.

Polynomials

Add together the coefficients of "like" terms. Like terms are those that have the same powers of the variables in the polynomials.

Yes, they can.

A homonym for the word "routes" is "roots." They are pronounced the same way but have different meanings.