Completing the Square: Why and When?

[Painguy]

So i just have a general knowledge question. not rly homework related

say u have a quadratic function or equation 4x2 – 2x – 5. Why would u have to complete the square in this situation? i know how to complete the square perfectly fine, but this was just bugging me.

I know that if ur graphing u complete the square to get it in the form a(x-h)^2 +c which makes it easier to visualize, but in the case of a quadratic equation i don't see why u can't just make everything equal to x as is.

 

[symbolipoint]

One completes the square to enable easy manual graphing and to help identify center, vertex, and other features of the graph.

 

[Mentallic]

Completing the square will also be used in maths later on with graphing circles, integration, inequality proofs etc.

Also, completing the square makes graphing a quadratic easier when there are no real roots.
If we solve $$x^2+2x+2=0$$ then the roots are $$x=-1\pm i$$ which doesn't really tell us anything about graphing it (other than it's completely above/below the x-axis), while $$(x+1)^2+1$$ is much clearer.

 

[verty]

Completing the square can be safer if you practice it, and it is good algebra practice to do it that way, if you have the time.

 

[vela]

So i just have a general knowledge question. not rly homework related

say u have a quadratic function or equation 4x2 – 2x – 5. Why would u have to complete the square in this situation? i know how to complete the square perfectly fine, but this was just bugging me.

I know that if ur graphing u complete the square to get it in the form a(x-h)^2 +c which makes it easier to visualize, but in the case of a quadratic equation i don't see why u can't just make everything equal to x as is.

Please note that one of the forum rules is:

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[Painguy]

Please note that one of the forum rules is:

oops Sorry about that. Also thanks for those who replied. I pretty much get it now.
Thanks for the help.