Matching Polynomials with Graphs

  1. The constant term of the polynomial shows the y-intercept of the graph.
  2. Look at the highest degree of the polynomial. The corresponding graph will have one less bend. For example, if the degree of the polynomial is 3, the corresponding graph shall have two bends.
  3. If all the zeros of the polynomial are real, then the corresponding graph will cross the x-axis as many times as the degree of the polynomial. For example, if the degree of the polynomial is 3, the corresponding graph shall cross the x-axis 3 times.
  4. If the zeros of the polynomial are visible because the polynomial is factored; then, match the zeros to the values where the graph crosses the x-axis.
  5. When two of the zeros are the same; then, the corresponding bend will simply touch the x-axis at that value.
  6. When two of the zeros are imaginary; then, the corresponding bend will not cross or even touch the x-axis.
  7. When all the zeros are real, the constant term of the polynomial shall be the product of the zeros.
  8. When there are two graphs matching the polynomial, take the root that is not common in both the graphs, and plug it in the polynomial. You will know if that zero belongs to the polynomial or not.

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