Homework Help

Express x^2 − 4x + 5 in the form (x + a)^2 + b and hence, or otherwise, write down...

user profile pic

saj-94 | (Level 1) Salutatorian

Posted September 20, 2013 at 9:32 AM via web

dislike 2 like

Express x^2 − 4x + 5 in the form (x + a)^2 + b and hence, or otherwise, write down the coordinates of the minimum point on the curve.

3 Answers | Add Yours

Top Answer

user profile pic

baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted September 20, 2013 at 9:39 AM (Answer #1)

dislike 1 like

`x^2 - 4x + 5`

To express in (x + a)^2 + b form we need to complete the square.

`(x^2 - 4x +c)^2 + 5` To find c, divide -4 by 2 and square it.

`(x^2 - 4x +4) + 5-4`

`(x - 2)^2 + 1`

Hence in the form (a+x)^2 + b we have:  `(x-2)^2 + 1`

This makes (2, 1) the minimum point.

user profile pic

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted September 20, 2013 at 9:39 AM (Answer #2)

dislike 1 like

`X^2-4x+5`

We know that;

`(x-2)^2 = x^2-4x+4`

`(x-2)^2+1 = x^2-4x+4+1`

`(x-2)^2+1 = x^2-4x+5`

`y=(x^2-4x+5)`

`y=(x-2)^2+1`

We know that `(x-2)>= 0` always .So the minimum of y will be obtained when `(x-2) =0`

`(x-2) = 0`

`X=2`

Minimum `y=(x-2)^2+1=(2-2)^2+1=1`

So the required answers are;

`x^2-4x+5 = (x-2)^2+1`
minimum point on curve is 1.

user profile pic

atyourservice | Student, Grade 10 | (Level 3) Valedictorian

Posted March 17, 2014 at 9:49 PM (Answer #3)

dislike 0 like

`x^2 - 4x + 5 `

`(x^2 - 4x) + 5`

use the formula (-b)/2  and the result squared will be c

`(-4)/2 = -2^2= 4`

`(x^2 -4x+4) + 5-4`

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

use the square root of a and c (use the sign between a and b), the number on the outside is the y point.

`(x-2)^2+1`

the minimum point would be 2,1 or just 1

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes