Hi,
You would probably be better off applying the signal to the inverting input resistor and applying half the required offset to the non inverting terminal. If you apply the signal to the non inverting terminal you get a gain of 2 which you probably dont want.
Keep in mind that the offset plus the peak can not go over the max output that you can get from the op amp you are using and it's power supply level. So if you have a plus and minus 5v input for example with a 1v offset voltage applied to the non inverting terminal, you'll get a triangle that goes from -3v to +7v. If you apply only a 0.5v offset then you'll see it go from -4 to +6v at the output.
If you really need to apply a voltage that must be equal to the actual offset, then use a differential amplifier connection. That way when you apply 1v you'll actually get a true 1v offset not a 2v offset.