Worksheet: Transforming Parabolas

In this worksheet, we will practice changing a quadratic equation so that its graph (a parabola) is shifted and/or compressed or dilated and vice versa.

Q1:

Describe the sequence of operations on the graph of 𝑦 = 𝑥 that produces the graph of 𝑦 = 𝑥 6 𝑥 + 1 4 .

  • Ashift 3 to the right then 14 up
  • Bshift 3 to the left then 5 up
  • Cshift 9 to the left then 14 up
  • Dshift 3 to the right then 5 up
  • Eshift 9 to the right then 5 up

Q2:

Which of the following graphs represents 𝑓 ( 𝑥 ) = ( 𝑥 1 ) + 2 2 ?

  • A(c)
  • B(a)
  • C(d)
  • D(b)

Q3:

Describe the sequence of operations on the graph of 𝑦 = 𝑥 that produces the graph of 𝑦 = 𝑥 + 𝑎 𝑥 + 𝑏 .

  • Ashift 𝑎 2 to the left then 𝑏 𝑎 2 up
  • Bshift 𝑎 2 to the right then 𝑏 𝑎 4 up
  • Cshift 𝑎 to the left then 𝑏 𝑎 2 up
  • Dshift 𝑎 2 to the left then 𝑏 𝑎 4 up
  • Eshift 𝑎 2 to the right then 𝑏 𝑎 2 up

Q4:

This is the graph of 𝑓 ( 𝑥 ) = 1 5 0 𝑥 5 .

Which of the following is the graph of 𝑦 = 1 5 0 ( 𝑥 + 1 0 ) 5 ?

  • A(c)
  • B(b)
  • C(a)

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