How do I convert y=x²-4x to y=a(x-p)² +q?

[sann]

How do I convert y=x²-4x to y=a(x-p)² +q?

How do I convert y=x²-4x to y=a(x-p)² +q?

 

[soroban]

Re: How do I convert y=x²-4x to y=a(x-p)² +q?

Hello, sann!

How do I convert \(\displaystyle \,y\:=\:x^2\,-\,4x\,\) to \(\displaystyle \,y\:=\:a(x\,-\,p)^2\,+\,q\) ?

We have: \(\displaystyle \:y\;=\;x^2\,-\,4x\)

Complete the square: \(\displaystyle \:y\;=\;x^2\,-\,4x\) + 4 - 4

And we have: \(\displaystyle \:y\;=\;(x\,-\,2)^2\,-\,4\)

. . with \(\displaystyle a\,=\,1,\\,=\,2,\:q\,=\,-4\)

 

[sann]

how did you get the 4?

 

[jwpaine]

how did you get the 4?

when completing the square, one of the steps is to take (1/2b)^2 from ax^2 + bx +c, and add it to both sides

b = 4,

so 1/2 of 4 = 2

2*2 = 4