Worksheet: Factors of Polynomial Functions from Their Graphs

In this worksheet, we will practice finding the equation of a polynomial function from its graph.

Q1:

Which of the following is a possible equation of the curve?

  • A 𝑦 = 1 5 𝑥 ( 𝑥 + 1 ) ( 𝑥 2 )
  • B 𝑦 = 1 7 𝑥 ( 𝑥 + 1 ) ( 𝑥 2 )
  • C 𝑦 = 1 7 𝑥 ( 𝑥 + 1 ) ( 𝑥 2 )
  • D 𝑦 = 1 5 𝑥 ( 𝑥 + 1 ) ( 𝑥 2 ) 2
  • E 𝑦 = 1 5 𝑥 ( 𝑥 + 1 ) ( 𝑥 2 ) 2 2

Q2:

Which of the following is the graph of 𝑓 ( 𝑥 ) = ( 𝑥 + 3 ) ( 𝑥 1 ) ( 𝑥 4 ) ?

  • A
  • B
  • C
  • D
  • E

Q3:

In ( ) a , the graph of 𝑓 ( 𝑥 ) = ( 𝑥 + 1 ) ( 𝑥 2 ) ( 𝑥 4 ) is represented. What is 𝑔 so that ( ) b is the graph of 𝑦 = 𝑓 ( 𝑥 ) 𝑔 ( 𝑥 ) ?

  • A 𝑔 ( 𝑥 ) = 𝑥 1
  • B 𝑔 ( 𝑥 ) = 2 𝑥 𝑥 1 2
  • C 𝑔 ( 𝑥 ) = 1 𝑥
  • D 𝑔 ( 𝑥 ) = 2 𝑥 + 𝑥 1 2
  • E 𝑔 ( 𝑥 ) = 𝑥 1

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