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

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, …

Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.

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 …

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.

Mar 13, 2025 · Why do the Graphs ‘Flatten Out’ as the Multiplicity Gets Higher? A small number (between −1 1 and 1 1), when multiplied by itself, gets even smaller (closer to zero).

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

Combining what we know about factors, degree, end behavior, the sign of the leading coeficient, and multiplicity gives us the ability to sketch polynomials written in factored form.

The number of times a given factor appears in the factored form of the equation of a polynomial is called the multiplicity. The zero associated with this factor, occurs twice. The graph passes …