The function \( f(x) = x^2 + 1 \) is a quadratic function in the standard form \( f(x) = ax^2 + bx + c \), where \( a = 1 \), \( b = 0 \), and \( c = 1 \).
Since the coefficient of \( x^2 \) (which is \( a \)) is positive, the parabola opens upward, and therefore it has a minimum point.
To find the x-coordinate of the minimum point, we can use the vertex formula for a parabola given by:
\[ x = -\frac{b}{2a} \]
Substituting the values of \( a \) and \( b \):
\[ x = -\frac{0}{2 \cdot 1} = 0 \]
Now, we can find the corresponding y-coordinate by substituting \( x = 0 \) back into the function \( f(x) \):
\[ f(0) = 0^2 + 1 = 1 \]
Therefore, the minimum point of the function \( f(x) = x^2 + 1 \) is at the coordinate point \( (0, 1) \).
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