SOLUTION: How do you write in the form of y=a(x-p)2+q from y=x2-6x+10?

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Question 17561: How do you write in the form of y=a(x-p)2+q from y=x2-6x+10?
Answer by rapaljer(4551) About Me  (Show Source):
You can put this solution on YOUR website!
Use the process called "completing the square". Given:
y=x%5E2+-+6x%2B10 you need to write this in the form y=+%28_____%29%5E2+%2B+___

You do this by taking the coefficient of x, which is -6, and take half of it, and square, which is +9. The trick is to add +9 and subtract 9 on the right side, in order to do what needs to be done, but keep the equation the same.

y+=+x%5E2+-6x+%2B9+-+9+%2B+10

Notice that the quantity x%5E2+-6x%2B9+ is a perfect square trinomial, and x%5E2+-+6x%2B9+=+%28x-3%29%5E2.

So, write:
y+=+%28x%5E2+-6x+%2B9%29+-+9+%2B+10
y+=+%28x-3%29%5E2+%2B1

That should do it! In your formula, a=1, p=3 and q = 1. Right??

Also, the vertex is at x=3 and y = 1, which is (p,q) = (3,1)!
+graph+%28300%2C300%2C+-10%2C10%2C-10%2C10%2C+x%5E2-6x%2B10%29
Is (3.1) the vertex of this parabola???

R^2 at SCC