Take half of the x coefficient -14 to get -7 . In other words, . (1/2) x (-14) = - 7
Now square -7 to get 49. In other words, (-7)^2=(-7) x (-7) = 49
x^2 - 14x+49-49+50 .Now add and subtract 49 . Make sure to place this after the "x" term. Notice how 49 -49 = 0. So the expression is not changed. Group the first three terms.
Factor to get .
Combine like terms.
So after completing the square, transforms to . So .
So is equivalent to .
So the equation is now in vertex form where , , and
Remember, the vertex of is (h,k).
So the vertex of is (7,1).
