How do you sketch the graph of #y=2(x-2)^2# and describe the transformation?

Question

Nathan Axel · Accepted Answer

There are two transformations applied to the graph: a vertical stretch by a scale factor of 2 and a translation 2 units to the right.

In order to sketch the graph, know that the vertex will be #(2,0)#. After this, plug values into the equation and plot them. Here are some points that should help you: #(0,8)# #(1,2)# #(2,0)# #(3,2)# #(4,8)# Here's the graph: graph{2(x-2)^2 [-8, 12, -1, 9]}

Jace Anderson · Answer

undefined To sketch the graph of $ y = 2(x-2)^2 $ and describe the transformation, follow these steps:

1. Identify the parent function: $ y = x^2 $.
2. The transformation $ (x-2)^2 $ indicates a horizontal shift of 2 units to the right.
3. The coefficient 2 outside the parentheses indicates a vertical stretch by a factor of 2.
4. Start by plotting key points of the parent function $ y = x^2 $.
5. Apply the horizontal shift by moving each point 2 units to the right.
6. Apply the vertical stretch by doubling the y-coordinate of each point.
7. Connect the points smoothly to sketch the graph.

The graph will be a vertically stretched parabola that is shifted 2 units to the right compared to the parent function $ y = x^2 $.