You should now know the generalizations of the parameter changes for the graphs of parabolas in the form y – k = a (x – h)2 or x – h = a (y – k)2.

In this last section, you will practice graphing by hand parabolas in this form. Creating a graph is a more demanding task than just recognizing the parameter changes in an equation.

video Watch the first video below explaining how to accurately and quickly graph a parabola in the form y – k = a (x – h)2.

Now watch this second video explaining how to graph a parabola in the form x - h = a (y - k)2.

Now that you have watched the two videos, let's try graphing some parabolas. Download and print the following activity sheet.

Conic Sections: Graphing Parabolas
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If you cannot print the activity sheet, just practice graphing the equations on your own graph or notebook paper. Try graphing each equation and check it before moving on to the next problem. Correct any mistakes you make.

Conic Sections: Graphing Parabolas

  1. y + 3 = –2 (x + 1)2
    2. Interactive popup. Assistance may be required.

    Check Your Answer

    • The vertex is (–1, –3)
    • The x-term is being squared, so the parabola opens up or down
    • a = –2, so the parabola opens down

    Close Pop Up
  2. 4x + 8 = (y + 1)2
    3. Interactive popup. Assistance may be required.

    Check Your Answer

    • The left side needs to be factored first
      4x + 8 = (y + 1)2
      4(x + 2) = (y + 1)2
    • Then both sides of the equation need to be divided by 4 to change the equation to standard form.
      x + 2 = 1 4 (y + 1)2
    • The vertex is (–2, –1)
    • The y-term is being squared, so the parabola opens left or right
    • a = 1 4 , so the parabola opens right

    Close Pop Up
  3. 4 – 2y = x2
    4. Interactive popup. Assistance may be required.

    Check Your Answer

    • The left side of the equation needs to be factored first
      4 – 2y = x2
      –2 (–2 + y) = x2
      –2 (y – 2) = x2
    • Then both sides of the equation need to be divided by –2 to change the equation to standard form.
      –2 (y – 2) = x2
      y – 2 = –1 2 x2
    • The vertex is (0, 2)
    • The x-term is being squared, so the parabola opens up or down
    • a = –1 2 , so the parabola opens down

    Close Pop Up
  4. x – 5 = –1 3 (y + 4)2
    5. Interactive popup. Assistance may be required.

    Check Your Answer

    • The vertex is (5, –4)
    • The y-term is being squared, so the parabola opens left or right
    • a = – 1 3 , so the parabola opens left

    Close Pop Up
  5. (x – 8)2 = 1 2 y
    6. Interactive popup. Assistance may be required.

    Check Your Answer

    • Both sides of the equation need to be multiplied by 2 to change the equation to standard form.
      (x – 8)2 = 1 2 y
      2 (x – 8)2 = y
      y = 2 (x – 8)2
    • The vertex is (8, 0)
    • The x-term is being squared, so the parabola opens up or down
    • a = 2, so the parabola opens up

    Close Pop Up
  6. 8 (y – 3)2 = –4x – 16
    7. Interactive popup. Assistance may be required.

    Check Your Answer

    • The right side of the equation needs to be factored first.
      8 (y – 3)2 = –4x – 16
      8 (y – 3)2 = –4 (x + 4)
    • Then both sides of the equation need to be divided by –4 to change the equation to standard form.
      8 (y – 3)2 = –4 (x + 4)
      –2 (y – 3)2 = x + 4
      x + 4 = –2(y – 3)2
    • The vertex is (–4, 3)
    • The y-term is being squared, so the parabola opens left or right
    • a = –2, so the parabola opens left

    Close Pop Up