Find the coordinate of the turning point of the curve y = x^2 - 10x + 7, by completing the square
First, we need to complete the square. We take the first part of the equation ignoring the constant ( + 7).
y = x2 - 10x , we want to change the form of this equation from x2 + ax + (a/2)2 into ( x + a/2 )2
y = ( x - 5 )2 - 25, what we did here was half the 10, and turn it into ( x - 5 )2 and we then subtracted the square of half of 10.
We then need to remember the constant + 7, so we add this back to the equation. y = ( x - 5 )2 - 25 + 7 = ( x - 5 )2 - 18.
The coordinate of the turning point is then ( 5, -18).
