Step-by-step explanation:
the general vertex form is
y = a(x - h)² + k
with (h, k) being the vertex.
after doing all the multiplications we get
y = a(x² - 2hx + h²) + k = ax² - 2ahx + ah² + k
our original equation is
y = x² - 6x + 17
and now we simply compare the cording parts :
ax² = x²
a = 1
-2ahx = -2hx = -6x
-2h = -6
h = -6/-2 = 3
ah² + k = 17
3² + k = 17
9 + k = 17
k = 8
so the vertex form is
y = (x - 3)² + 8
