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. \( f(x)=(x-(\square))^{2}+(\square) \)

We start with the quadratic function   f(x) = x² – 8x + 14. To complete the square, follow these steps: 1. Group the x-terms:   x² – 8x  +14 2. Find the number needed to complete the square. Take half of the coefficient of x (which is –8) to get –4, and then square it:   (–4)² = 16. 3. Add and subtract 16 inside the expression:   f(x) = (x² – 8x + 16) – 16 + 14 4. Rewrite the trinomial as a perfect square:   x² – 8x + 16 = (x – 4)² 5. Combine the constants:   –16 + 14 = –2. Thus, the function in completed square form is:   f(x) = (x – 4)² – 2 In the expression f(x) = (x – (□))² + (□), the correct numbers are 4 and –2, so that   f(x) = (x – 4)² – 2. Graphing by shifting: • The vertex of the parabola is at (4, –2). • Compared to the basic parabola y = x², the graph is shifted 4 units to the right and 2 units downward. • The axis of symmetry is the vertical line x = 4. These shifts determine the position and shape of the graph.