2.5.1

Graphs of Polynomials

Test yourself

Drawing Graphs of Polynomials

Follow these steps to make drawing graphs of polynomial simple.

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Intercepts

  • The degree of the leading term of the polynomial gives the maximum number of roots or xx-intercepts.
    • x4+2x12x^4+2x-12 has two real roots and so two xx-intercepts.
  • The yy-intercepts of the graph are found by substituting x=0x=0 into the polynomial.
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End behavior

  • The end behavior of a graph is how it behaves for very large or very small values of xx.
  • The end behavior is determined by both the degree and coefficient of the leading term.
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Complete a table of values

  • Make a table of values for y when x is equal to different numbers in a given range.
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Connect the points

  • Connect the points plotted on the graph with a smooth curve, comparing with what you know about the graph's shape from its equation.

Jump to other topics

1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

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