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 are given the quadratic function   f(x) = x² – 8x + 14. Step 1. To complete the square, start by focusing on the quadratic and linear terms. Write:   x² – 8x = x² – 8x + ( ? ) We need to add and subtract the same value to complete the square. Take half of the coefficient of x (which is –8), half is –4, and square it:   (–4)² = 16. Step 2. Add and subtract 16 inside the function:   f(x) = (x² – 8x + 16) – 16 + 14      = (x – 4)² – 2. Thus, in the complete square form   f(x) = (x – (4))² + (–2). Step 3. Graphing by shifting: • Start with the basic parabola y = x². • Shift it right by 4 units (because of (x – 4)²). • Shift it downward by 2 units (because of –2). The vertex of the parabola is at (4, –2). So, the completed square expression is:   f(x) = (x – 4)² – 2. And the graph is obtained by shifting the graph of y = x² right 4 units and down 2 units.