How to write f(x)=x^2+4x+1 in vertex form?

Nathanial Frost

Nathanial Frost

Answered question

2023-02-18

How to write f ( x ) = x 2 + 4 x + 1 in vertex form?

Answer & Explanation

Rhys Murphy

Rhys Murphy

Beginner2023-02-19Added 3 answers

The equation in vertex form is f ( x ) = a ( x - h ) 2 + k
Here, we have f ( x ) = x 2 + 4 x + 1 , so we have a = 1
So for converting to this form, we complete the square using ( x + a ) 2 = x 2 + 2 a x + a 2 for which we have to identify a and then add and subtract a 2 Thus,
f ( x ) = x 2 + 2 × 2 × x + 2 2 ̲ - 2 2 + 1
= ( x + 2 ) 2 - 4 + 1
= ( x - ( - 2 ) ) 2 - 3

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?