Final answer:
The quote from President Obama's speech that best explains why he believes the U.S. will survive and thrive through changing times is: b) Change is inevitable, but our shared values endure.
Step-by-step explanation:
The quote from President Obama's speech that best explains why he believes the U.S. will survive and thrive through changing times is b) Change is inevitable, but our shared values endure. This quote emphasizes the belief that while change is a constant in life, it is the enduring values of the American people that will allow the country to overcome challenges and continue to thrive. By acknowledging the inevitability of change and the resilience of shared values, President Obama expresses his confidence in the future of the United States.