Answer:
(3, 1)
Explanation:
First, find the equation of the axis of symmetry, which passes vertically through the vertex. The coefficients of f(x) = x^{2} - 6x + 10 are a = 1, b = -6 and c = 10. The formula for the axis of symmetry is
-b -(-6)
x = ------- and in this particular case, x = -------- = 3
2a 2(1)
Next, use this x-vaue (3) as the divisor in synthetic division. The value of the remainder represents the y coordinate of the vertex.
3 1 -6 10
3 -9
-------------------
1 -3 1
Thus, the coordinates of the vertex are (3, 1).