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.[br][img]data:image/png;base64,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[/img][br][br][img]data:image/png;base64,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[/img][br][br]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?[br] a. vertex at (0, 11) and graph opens up[br] b. vertex at (7, 11) and graph opens up[br] c. vertex at (7, -3) and graph opens down[br][br]Use [color=#3c78d8][url=https://www.desmos.com/calculator]desmos.com[/url][/color] to verify your predictions. Adjust your equations if necessary.[br]
Kiran graphed the equation y = x² + 1 and noticed that the vertex is at (0, 1). [br]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).[br] [br]Next, he graphed the equation y = x²+ 2x + 1, observed that the vertex is at (-1, 0). [br]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).”[br][br]Do you agree with Kiran? Explain or show your reasoning.
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Information: A.6.17.2 Shifting the Graph