Finally, we are going to explore how the graph of y = ax² is affected when the value of a is less than 0.

Click on the link below to access an online graphing calculator.

Graphit

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

Directions:

1. Enter x² in the y(x) field and then click on Plot/Update to graph the equation.
2. Go to the next line in the y(x) field and enter -x². Then click on Plot/Update.
3. Go to the 3rd line in the y(x) field and enter 2x². Then click on Plot/Update.
4. Go to the 4th line in the y(x) field and enter -2x². Then click on Plot/Update.
5. Go to the 5th line in the y(x) field and enter 1 3 x². Then click on Plot/Update. (You can enter the fraction by using the / key on your keyboard.)
6. Go to the 6th line in the y(x) field and enter - 1 3 x². Then click on Plot/Update.
7. In your notes, describe how changing the coefficient of x from "1" to a number less than 0 affects the graph. (Use the words narrower or wider.)

Check Your Answer

When the value of a is a less than 0, the graph of the function is a reflection across the x-axis of the original function. The parabola gets narrow or wide depending on the value of a.