Find the minimum value of the function \( f(x)=x^{2}-2 x+6 \) to the nearest hundredth.

To find the minimum value of the quadratic function \( f(x) = x^2 - 2x + 6 \), we can follow these steps: 1. **Identify the coefficients**: - \( a = 1 \) (coefficient of \( x^2 \)) - \( b = -2 \) (coefficient of \( x \)) - \( c = 6 \) (constant term) 2. **Find the x-coordinate of the vertex**: The vertex of a parabola given by \( f(x) = ax^2 + bx + c \) is at: \[ x = -\frac{b}{2a} \] Plugging in the values: \[ x = -\frac{-2}{2 \times 1} = 1 \] 3. **Compute the minimum value by plugging \( x = 1 \) back into the function**: \[ f(1) = (1)^2 - 2(1) + 6 = 1 - 2 + 6 = 5 \] So, the minimum value of the function \( f(x) = x^2 - 2x + 6 \) is **5.00** when rounded to the nearest hundredth. **Answer:** 5.00