Let's look at how the equations of y = x2 + c move the parabola.

Click on the link below to access an online graphing calculator. Then follow the directions below to complete the exercise.

This activity might not be viewable on your mobile device.Interactive exercise. Assistance may be required. Online Graphing Calculator

At any time, you may click on "Show Tabular Data" to see a table of values.

  1. Enter x2 + 3 in the y(x) field and then click on Plot/Update to graph the equation.
  2. Go the next line in the y(x) field and enter x2 – 1. Then click on Plot/Update.

In your notes, answer the following questions.

  1. How many units down did the parabola move? Interactive popup. Assistance may be required.

    Check Your Answer

    4 units.

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  2. Shift the equation y = x2 – 3 up 7 units, what is the new equation? Interactive popup. Assistance may be required.

    Check Your Answer

    y = x2 + 4 because -3 + 7 = +4

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In your notes, determine how the equation or the graph of each quadratic function will change.

  1. How would the graph of the function y = x2 + 3 change if the function were changed to y = x2 + 5?
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    Check Your Answer

    The graph (or parabola) would shift up 2 units.

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  2. If the graph of the function y = x2 + 7 is changed to y = x2 – 1, how would you describe the shift in the vertex of the parabola?
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    Check Your Answer

    The shift would be down 8 units.

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  3. If the graph of y = x2 – 5 is shifted up 2 units, what equation will describe the new graph?
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    Check Your Answer

    y = x2 – 3

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  4. If the graph of y = x2 + 1 is shifted down 2 units, what equation will describe the new graph?
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    Check Your Answer

    y = x2 – 1

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