Q:

How to amplify and offset the voltage in an opamp?

I need to amplify a voltage, which comes from a DAC and is 0-2.5V and scale it 0-25V in an operational amplifier. After amplified, I need to offset it -1.25V, so the final voltage is -1.25 to 23.75V. In other words, being an operational amplifier, I want to do the y=ax+b operation. with a=10, and b=-1.25V
I thought of 2 different ways of doing this.

The first idea I had is to use a second amplifier as a summing amplifier, with a fixed -1.25V voltage. 
The second idea is to use a 1.2V zener in series with the output, along with a biasing resistor to -V.

Why do I want this? I want to set the ADJ pin in an LM338 voltage regulator from an MCU. LM338 out is ADJ+1.25V. If ADJ is -1.25V then the output is 0V.

A:

You can use a differential amplifier

As you can see from the shown equation VR is just an offset and doesn't get amplified so set the resistors for a gain of 10 , connect GND to V1 and -1.25 to VR
The reply here shows an alternative solution that doesn't need a 1.25v reference but it needs a negative rail voltage to supply the opamp

