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You can do this by using "Conditions" function in our form builder. You can learn more about it here: https://www.jotform.com/help/57-Smart-Forms-Using-Conditional-Logic.
For a quick guide, you can check the screenshots below.
1. I added a radio group with 3 options and a text field.
2. After clicking the conditions in the toolbar you'll then be directed to the Conditions Wizard, I'll choose the 1st option as I would like to display the text field when radio button option 2 is selected.
3. Here's my rules and actions.
Make sure you "Save" all the changes. Here's a demo form that I have: http://form.jotformpro.com/form/50223777316959
Let us know if you need more assistance on this.