Use the graph of the function of degree 6 to identify the zeros of the function and their possible multiplicities. The polynomial function is of degree n which is 6. The sum of the multiplicities must be 6.

Demonstrates how to recognize the multiplicity of a zero from the graph of its polynomial. Explains how graphs just "kiss" the x-axis where zeroes have even multiplicities.

Let's look at the graph of a function that has the same zeros, but different multiplicities. For example, consider g (x) = (x 1) 2 (x 4) . Notice that for this function 1 is now a double zero, while 4 is a single …

Algebra 2 will build on the topics of zeros, multiplicity, end behavior, and transformations as they relate to graphing. If you need to review your graphing skills, see the "refresh" listings under Function Graphs.

Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.

For zeros with even multiplicities, the graphs touch or are tangent to the x -axis. For zeros with odd multiplicities, the graphs cross or intersect the x -axis.

May 16, 2025 · Discover how zeros and multiplicity shape polynomial graphs in Algebra I, with step-by-step root-finding and graph interpretation.

Once we know where the graph is going we can find the x-intercepts to obtain a general shape of the graph. We will use the multiplicity of the power of each factor to determine if the graph...

Mar 13, 2025 · It is impossible to get a single to-scale graph of P P that clearly shows the interesting behavior near all the zeroes. (The next section discusses this in more detail.)

Multiplicity is just the degree (exponent) of each factor, or the amount of times a factor appears. If the multiplicity is even, the graph will “bounce” off the x-axis where that factor is zero. And if the …