This can be done using the DxDiag tool on your computer. Open your Start menu and type dxdiag into the Run box. This will open a diagnostic window on your computer. Click on the Save All Information button and save the text file that this tool creates somewhere accessible, such as your Desktop.
Open the text file, then press Control + F to search. Enter Miracast into the search box, then click on Find Next. You should have 3 results, and you will want to see that Miracast is listed as available or supported for the first 2 results.