Use this eTool to support a class discussion about the equation y = a(x − h)² + k.

• Identify which parameter (a, h, or k) affects the orientation, vertical shift, horizontal shift, vertical stretch, and vertical compression of the graph compared to the graph of the parent function y = x^2.
• ^{What values stretch the graph vertically?  Compress the graph vertically?  Why do those values have these impacts?}
• ^{What values cause the graph to flip vertically?}
• ^{What values cause the graph to shift to the left?  To the right?  Why?}
• ^{What values cause the graph to shift up or down?  Why?}
• ^{Are there points on your graph that connect to specific parameters in the equation?  Explain.}

Click the blue points on the sliders and drag (horizontally) to change the parameters.