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Graphs of Polynomials

Maths: Edexcel A Level Pure Maths, topic 2.5.1

Drawing Graphs of Polynomials

Follow these steps to make drawing graphs of polynomial simple.

Intercepts

Intercepts

  • The degree of the leading term of the polynomial gives the maximum number of roots or xx-intercepts.
  • x4+2x−12x^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.
End behavior

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.
End behavior

End behavior

Complete a table of values

Complete a table of values

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

Plot the points on a graph

Connect the points

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.

Test yourself on Graphs of Polynomials

  • What is the largest number of x-intercepts a cubic graph can have?

  • Which value of x has no corresponding value of y for y=1x\frac{1}{x}?

  • The table of values for the polynomial y= x3 + x2 + x + 1 is shown below. What is the value of X?

  • The table of values for the polynomial y= x3 + x2 + x + 1 is shown below. What is the value of Y?

  • The table of values for the polynomial y= x3 + x2 + x + 1 is shown below. What is the value of Z?

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