Question

Which function in vertex form is equivalent to f(x) = x2 + x +1?

f(x) = (x + one-quarter) squared + three-quarters
f(x) = (x + one-quarter) squared + five-quarters
f(x) = (x + one-half) squared + three-quarters
f(x) = (x + one-half) squared + five-quarters

Answer 1

f(x) = (x + 1/2)^2 + 3/4

Reason: x^2 + x + 1 = (x + 1/2)^2 − 1/4 + 1 = (x + 1/2)^2 + 3/4, so the third choice is correct.