Question

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

Answer 1

F(x) = (x +1/2)² +3/4

Answer 2

Answer:

The function in vertex form is  $f(x)=(x-(-\frac{1}{2}))^2+\frac{3}{4}$  

Step-by-step explanation:

Given: Function  $f(x)=x^2+x+1$  

We have to write the given function  $f(x)=x^2+x+1$ in vertex form.

Consider the given function $f(x)=x^2+x+1$  

Using algebraic identity $(a+b)^2=a^2+b^2+2ab$

Comparing a = x , 2ab = x

Also, 2b = 1 ⇒$b=\frac{1}{2}$

Add and subtract $b^2=\frac{1}{4}$ , we get,

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

Simplify, we have,

$f(x)=(x+\frac{1}{2})^21-\frac{1}{4}$  

Simplify, we have,

$f(x)=(x+\frac{1}{2})^2+\frac{3}{4}$  

Thus, The function in vertex form is  $f(x)=(x-(-\frac{1}{2}))^2+\frac{3}{4}$