Question

Which function in vertex form is equivalent to f(x) = x^2 + x +1?​

Answer 1

Answer:

C

Step-by-step explanation:

x² + x + 1

x² + 2(x)(½) + (½)² - (½)² + 1

(x + ½)² - ¼ + 1

(x + ½)² + ¾

Answer 2

Answer:

C

Step-by-step explanation:

Given

f(x) = x² + x + 1

To obtain the function in vertex form use the method of completing the square.

Add/ subtract ( half the coefficient of the x- term )² to x² + x

f(x) = x² + 2($\frac{1}{2}$ )x + $\frac{1}{4}$ - $\frac{1}{4}$ + 1

     = (x + $\frac{1}{2}$ )² + $\frac{3}{4}$ → C