Question

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

○ f(x) = (x + 1/ 1³² + 1 ²1/0
3
4
○ f(x) = (x + 1)² + 2/1/2
○ f(x) = (x + ²/2 1²³ + ²/
4
5
f(x) = (x + 1/2-1² + ²/1/2
4

Answer 1

`\left( x+(1)/(2) \right)^(2) + (3)/(4)`

Explanation:

NOTE :

`x^2+ax=\left( x+(a)/(2) \right)^(2) -\left( (a)/(2) \right)^(2)`

………………………………………

f(x) = x² + x +1

`=x^(2)+2* (x)/(2) +1`

`=\left( x+(1)/(2) \right)^(2) -\left( (1)/(2) \right)^(2) +1`

`=\left( x+(1)/(2) \right)^(2) - (1)/(4)+1`

`=\left( x+(1)/(2) \right)^(2) + (3)/(4)`