Explanation:
vertex form is
y = (x - h)² + k
with (h, k) being the vertex.
this is with the multiplications done
y = x² - 2hx + h² + k
and now we compare this to our original equation
y = x² - 10x + 14
-10x = -2hx
-10 = -2h
h = 5
h² + k = 14
25 + k = 14
k = -11
the vertex form is
y = (x - 5)² - 11
and for
y = x² - 10x
h = 5
25 + k = 0
k = -25
the vertex form is
y = (x - 5)² - 25