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

User Grreeenn
by
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2 Answers

4 votes

Answer:

The function in vertex form is
f(x)=(x-(-(1)/(2)))^2+(3)/(4)

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=(1)/(2)

Add and subtract
b^2=(1)/(4) , we get,


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

Simplify, we have,


f(x)=(x+(1)/(2))^21-(1)/(4)

Simplify, we have,


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

Thus, The function in vertex form is
f(x)=(x-(-(1)/(2)))^2+(3)/(4)

User Folex
by
8.0k points
6 votes
f(x) = (x +1/2)² +3/4
Which function in vertex form is equivalent to f(x) = x2 + x +1?-example-1
User Dylan Cristy
by
8.0k points

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