Manual (M) is the best choice and your shooting modes are as below:
• Auto shooting mode
• Program (auto)
• Shutter Priority Auto
• Aperture Priority Auto
• Manual
• Movie mode
• Scene mode
• High-sensitivity shooting mode
• Anti-shake mode
You might want to use the Auto ISO feature (allows the camera to determine proper exposures from 64 through 800) but you can go up to as high as 3200 if the situation permits.
Your zoom capability is 4x so you may find that for fireworks, your camera is ideally suited.
The problem is, you didn't say 'TRIPOD' and, shooting fireworks is only done properly with one.
You have up to an 8 second shutter time - enough time to record some awesome light displays and, with scene modes that include Face-priority AF, Portrait, Landscape, Sports, Night Portrait, Party/Indoor, Beach/Snow, Sunset, Dusk/Dawn, Night Landscape, Close up, Museum, Fireworks show, Copy, Back Light and Panorama Assist, you might want to use Night Landscape as your scene mode.
Have fun but do get a tripod for this or you will be sick with the results you get.
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