The vertex of the graph of a quadratic function in the standard form y = ax^2 + bx + c can be found using the vertex formula.
In this case, our equation is y = x^2 + 2x + 3, where a = 1, b = 2, and c = 3.
The x-coordinate of the vertex is given by the formula:
x = -b / (2a)
Substituting the values of b and a:
x = -2 / (2 * 1) = -1
Now, we need to find the y-coordinate by substituting x = -1 back into the original equation:
y = (-1)^2 + 2(-1) + 3
y = 1 – 2 + 3 = 2
Therefore, the vertex of the graph is at the point (-1, 2).