Complete the square of the given quadratic expression. Then, graph the function using the technique of shifting. \( f(x)=x^{2}-8 x+14 \) Complete the square by entering the correct numbers into the expression below. \( f(x)=(x-(\square))^{2}+(\square) \)

To complete the square for the quadratic expression \( f(x) = x^2 - 8x + 14 \), we follow these steps: 1. Take the coefficient of \( x \) (which is -8), divide it by 2 to get -4, and then square it to get 16. 2. Rewrite the quadratic as \( f(x) = (x^2 - 8x + 16) - 16 + 14 \). 3. Simplifying gives us \( f(x) = (x - 4)^{2} - 2 \). Now, we can fill in the blanks: \( f(x) = (x - (4))^{2} + (-2) \). For graphing, this represents a parabola that opens upwards, with its vertex shifted to the point (4, -2) on a Cartesian plane. To visualize, start by plotting the vertex and then sketching the parabola by using points on either side of the vertex and noting its symmetric nature around the vertical line \( x = 4 \).