Purpose of completing the square in quadratic equations (1 Viewer)

[Joshmosh2]

Greetings,
By completing the square, what have i accomplished? It seems that completing the square only adds more steps to the problem
For example, an equation like y=x^2-2x, the x and y intercepts can be found instantly
However, when a question asks to complete the square, then sketch the graph, what benefits come from doing so?
y=(x-1)^2-1 looks like a mess.

 

[Carrotsticks]

One of the most important features of the parabola is its vertex.

By completing the square, you can literally just read the coordinates of the vertex!

So in your example, y=(x-1)^2-1, the 'standard' parabola y=x^2 has been

1. Shifted to the right by 1 unit

2. Shifted down by 1 unit

So the vertex is simply (1,-1).

------------------------------------------

Another example is say y=(x+3)^2+2.

This tells us that y=x^2 has been

1. Shifted left by 3 units

2. Shifted up by 2 units

So the vertex is simply (-3,2)

------------------------------------------

Completing the square will also come in super handy later on when it comes to a topic called Integration.

Those are just a few of its many uses!

 

[SpiralFlex]

Good question,

 

[Joshmosh2]

ahh, i guess that would be convenient instead of f(-b/2a). Thanks