Question

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

Answer 1

C

Explanation:

x² + x + 1

x² + 2(x)(½) + (½)² - (½)² + 1

(x + ½)² - ¼ + 1

(x + ½)² + ¾

Answer 2

C

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(
`(1)/(2)` )x +
`(1)/(4)` -
`(1)/(4)` + 1

= (x +
`(1)/(2)` )² +
`(3)/(4)` → C