A.6.17.2 Shifting the Graph

As a reminder, here is the graph of y = x². The vertex is at the origin and teh graph opens up. You can see several points plotted on either side of the vertex. How would you change the equation y = x² so that the vertex of the graph of the new equation is located at the following coordinates and the graph opens as described? a. vertex at (0, 11) and graph opens up b. vertex at (7, 11) and graph opens up c. vertex at (7, -3) and graph opens down Use desmos.com to verify your predictions. Adjust your equations if necessary.

Kiran graphed the equation y = x² + 1 and noticed that the vertex is at (0, 1). He changed the equation to y = (x - 3)² + 1 and saw that the graph shifted 3 units to the right and the vertex is now at (3, 1). Next, he graphed the equation y = x²+ 2x + 1, observed that the vertex is at (-1, 0). Kiran thought, “If I change the squared term x² to (x - 5)², the graph will move 5 units to the right and the vertex will be at (4, 0).” Do you agree with Kiran? Explain or show your reasoning.