f(x) = 2x² - 8x + 7=2(x²-4x) + 7
We are going to use formula a²-2ab+b² = (a-b)² to complete the square.
f(x)= 2(x² -2*2x+2²-2²)+7
f(x)=2(x² -2*2x+2²) -2*2² +7
f(x)=2(x-2)²- 1
Answer is D.
We can see that f(x) = 2x² - 8x + 7 and f(x)=2(x-2)²- 1 are the same on the graph.