How to Use Completing the Square to Write a Quadratic Expression in Vertex Form

[enigmatatki]

Hello =D I was doing an IB Project for math... and this question popped out.

Describe a method of writing the quadratic expression x2 + bx + c in the form
(x – h) 2 + g


I know how to do them (complete the square) but I don't know how to describe them.

for example, where does h and g pop out?

If you guys could help me... it would mean so much to me =D

thanx!

 

[Dr Transport]

look at x^{2} + bx +(b/2)^{2} - (b/2)^{2} + c = (x+b/2)^{2} +c - (b/2)^{2} which completes the square...

 

[Tide]

Hello =D I was doing an IB Project for math... and this question popped out.

Describe a method of writing the quadratic expression x2 + bx + c in the form
(x – h) 2 + g


I know how to do them (complete the square) but I don't know how to describe them.

for example, where does h and g pop out?

If you guys could help me... it would mean so much to me =D

thanx!

You might be interested in the geometric interpretation - completing the square really IS completing the square!

(I had to do some serious editing and compression to get it to fit - hope it works!)