Final answer:
The vertex of the given quadratic function is (3/2, -17/4).
Step-by-step explanation:
The vertex of a quadratic function in the form y = ax^2 + bx + c is given by the coordinates (h, k), where h and k can be found using the formula h = -b/2a and k = f(h), where f(h) represents substituting h into the equation for x.
In the given equation y = x^2 - 3x + 2, a = 1, b = -3, and c = 2.
Plugging these values into the formulas, we can find the vertex as follows:
h = -(-3)/(2*1) = 3/2
k = (3/2)^2 - 3(3/2) + 2
= 1/4 - 9/2 + 2
= -17/4
Therefore, the vertex of the function is (3/2, -17/4).