Use technology to find points and then graph the function \( y=(x-1)^{2} \), following the instructions below.

Below is one way to “use technology” (for example, a graphing calculator, GeoGebra, Desmos, etc.) to explore and graph the function   y = (x – 1)². Step 1. Create a Table of Values. Choose several x-values and compute the corresponding y-values. For example:   • x = –2  →  y = (–2 – 1)² = (–3)² = 9   • x = –1  →  y = (–1 – 1)² = (–2)² = 4   • x = 0  →  y = (0 – 1)² = (–1)² = 1   • x = 1  →  y = (1 – 1)² = (0)² = 0   • x = 2  →  y = (2 – 1)² = (1)² = 1   • x = 3  →  y = (3 – 1)² = (2)² = 4   • x = 4  →  y = (4 – 1)² = (3)² = 9 You now have this table:   x  | y   ————————   –2 | 9   –1 | 4    0 | 1    1 | 0    2 | 1    3 | 4    4 | 9 Step 2. Graph the Function Using Technology. 1. Enter the function y = (x – 1)² into your graphing tool. 2. Use the table of points to verify that the graph has the expected points. Notice that the point (1, 0) is the vertex of the parabola. 3. Adjust the viewing window if necessary so you can see the vertex and several points on each “side” of the graph. A window with x-values from –3 to 5 and y-values from –1 to 10 should work well. Step 3. Analyze the Graph. When you graph y = (x – 1)², you should see:  • A parabola that opens upward.  • The vertex located at (1, 0).  • Symmetry about the vertical line x = 1.  • Points such as (–2, 9) and (4, 9) lying on the graph, confirming the symmetry. This process (creating a table of values and using a graphing tool) is a common approach when using technology to study functions. Feel free to explore other x-values or adjust the window to further interact with the graph!