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Worksheet: Equation of a Polynomial from a Sketch

Q1:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = βˆ’ ( π‘₯ βˆ’ 7 ) 3
  • B 𝑦 = ( π‘₯ + 7 ) 3
  • C 𝑦 = βˆ’ ( π‘₯ + 7 ) 3
  • D 𝑦 = ( π‘₯ βˆ’ 7 ) 3
  • E 𝑦 = π‘₯ + 7 3

Q2:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = ( π‘₯ βˆ’ 1 ) ( π‘₯ + 3 ) ( π‘₯ βˆ’ 3 )
  • B 𝑦 = ( π‘₯ + 1 ) ( π‘₯ + 3 ) ( π‘₯ βˆ’ 3 )
  • C 𝑦 = βˆ’ ( π‘₯ βˆ’ 1 ) ( π‘₯ + 3 ) ( π‘₯ βˆ’ 3 )
  • D 𝑦 = βˆ’ ( π‘₯ + 1 ) ( π‘₯ + 3 ) ( π‘₯ βˆ’ 3 )
  • E 𝑦 = βˆ’ π‘₯ ( π‘₯ + 1 ) ( π‘₯ + 3 )

Q3:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = βˆ’ ( π‘₯ + 7 ) ( π‘₯ + 1 ) 2
  • B 𝑦 = ( π‘₯ + 7 ) ( π‘₯ + 1 ) 2
  • C 𝑦 = ( π‘₯ βˆ’ 1 ) ( π‘₯ βˆ’ 7 ) 2
  • D 𝑦 = ( π‘₯ βˆ’ 7 ) ( π‘₯ βˆ’ 1 ) 2
  • E 𝑦 = βˆ’ ( π‘₯ + 1 ) ( π‘₯ + 7 ) 2

Q4:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = βˆ’ ( π‘₯ βˆ’ 2 ) ( π‘₯ + 5 )
  • B 𝑦 = ( π‘₯ + 2 ) ( π‘₯ βˆ’ 5 )
  • C 𝑦 = ( π‘₯ βˆ’ 2 ) ( π‘₯ + 5 )
  • D 𝑦 = βˆ’ ( π‘₯ + 2 ) ( π‘₯ βˆ’ 5 )
  • E 𝑦 = βˆ’ ( π‘₯ + 2 ) ( π‘₯ + 5 )

Q5:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = βˆ’ ( π‘₯ βˆ’ 2 ) ( π‘₯ + 4 )
  • B 𝑦 = ( π‘₯ βˆ’ 2 ) ( π‘₯ + 4 )
  • C 𝑦 = βˆ’ ( π‘₯ + 2 ) ( π‘₯ βˆ’ 4 )
  • D 𝑦 = ( π‘₯ + 2 ) ( π‘₯ βˆ’ 4 )
  • E 𝑦 = ( π‘₯ βˆ’ 2 ) ( π‘₯ βˆ’ 4 )

Q6:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = ( π‘₯ + 5 ) ( π‘₯ βˆ’ 5 ) 3
  • B 𝑦 = βˆ’ ( π‘₯ βˆ’ 5 ) ( π‘₯ + 5 ) 3
  • C 𝑦 = ( π‘₯ βˆ’ 5 ) ( π‘₯ + 5 ) 3
  • D 𝑦 = βˆ’ ( π‘₯ + 5 ) ( π‘₯ βˆ’ 5 ) 3
  • E 𝑦 = ( π‘₯ + 5 ) ( π‘₯ βˆ’ 5 ) 3 2

Q7:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = βˆ’ ( π‘₯ + 7 ) ( π‘₯ + 2 ) ( π‘₯ βˆ’ 2 ) ( π‘₯ βˆ’ 8 )
  • B 𝑦 = ( π‘₯ + 7 ) ( π‘₯ + 2 ) ( π‘₯ βˆ’ 2 ) ( π‘₯ βˆ’ 8 )
  • C 𝑦 = βˆ’ ( π‘₯ βˆ’ 7 ) ( π‘₯ + 2 ) ( π‘₯ βˆ’ 2 ) ( π‘₯ + 8 )
  • D 𝑦 = ( π‘₯ βˆ’ 7 ) ( π‘₯ + 2 ) ( π‘₯ βˆ’ 2 ) ( π‘₯ + 8 )
  • E 𝑦 = ( π‘₯ βˆ’ 7 ) ( π‘₯ + 2 ) ( π‘₯ βˆ’ 2 ) ( π‘₯ βˆ’ 8 )

Q8:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = βˆ’ ( π‘₯ + 2 ) ( π‘₯ βˆ’ 3 ) ( π‘₯ βˆ’ 5 )
  • B 𝑦 = ( π‘₯ βˆ’ 2 ) ( π‘₯ + 3 ) ( π‘₯ + 5 )
  • C 𝑦 = ( π‘₯ + 2 ) ( π‘₯ βˆ’ 3 ) ( π‘₯ βˆ’ 5 )
  • D 𝑦 = βˆ’ ( π‘₯ βˆ’ 2 ) ( π‘₯ + 3 ) ( π‘₯ + 5 )
  • E 𝑦 = βˆ’ ( π‘₯ βˆ’ 2 ) ( π‘₯ βˆ’ 3 ) ( π‘₯ βˆ’ 5 )

Q9:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = ( π‘₯ + 2 ) ( π‘₯ + 2 ) 2 2
  • B 𝑦 = βˆ’ ( π‘₯ + 2 ) ( π‘₯ βˆ’ 2 ) 2 2
  • C 𝑦 = ( π‘₯ βˆ’ 2 ) ( π‘₯ βˆ’ 2 ) 2 2
  • D 𝑦 = ( π‘₯ + 2 ) ( π‘₯ βˆ’ 2 ) 2 2
  • E 𝑦 = βˆ’ ( π‘₯ + 2 ) ( π‘₯ + 2 ) 2 2

Q10:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = ( π‘₯ βˆ’ 4 ) ( π‘₯ + 4 ) 2
  • B 𝑦 = βˆ’ ( π‘₯ + 4 ) ( π‘₯ βˆ’ 4 ) 2
  • C 𝑦 = βˆ’ ( π‘₯ βˆ’ 4 ) ( π‘₯ + 4 ) 2
  • D 𝑦 = ( π‘₯ + 4 ) ( π‘₯ βˆ’ 4 ) 2
  • E 𝑦 = π‘₯ ( π‘₯ + 4 ) ( π‘₯ βˆ’ 4 )

Q11:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = ( π‘₯ βˆ’ 5 ) ( π‘₯ + 4 ) 2 2
  • B 𝑦 = βˆ’ ( π‘₯ + 5 ) ( π‘₯ βˆ’ 4 ) 2 2
  • C 𝑦 = βˆ’ ( π‘₯ βˆ’ 5 ) ( π‘₯ + 4 ) 2 2
  • D 𝑦 = ( π‘₯ + 5 ) ( π‘₯ βˆ’ 4 ) 2 2
  • E 𝑦 = ( π‘₯ βˆ’ 5 ) ( π‘₯ βˆ’ 4 ) 2 2

Q12:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = βˆ’ π‘₯ ( π‘₯ βˆ’ 5 ) ( π‘₯ + 6 )
  • B 𝑦 = π‘₯ ( π‘₯ βˆ’ 5 ) ( π‘₯ + 6 )
  • C 𝑦 = βˆ’ π‘₯ ( π‘₯ + 5 ) ( π‘₯ βˆ’ 6 )
  • D 𝑦 = π‘₯ ( π‘₯ + 5 ) ( π‘₯ βˆ’ 6 )
  • E 𝑦 = π‘₯ ( π‘₯ + 5 ) ( π‘₯ + 6 )