# Lesson 17

Parameters and Graphs

- Let’s talk about moving graphs around the plane.

### 17.1: Which One Doesn’t Belong: Triangles

Each figure shows triangle \(PQR\), and its image after a transformation, \(P'Q'R'\). Which one doesn’t belong?

### 17.2: Describe the Change

- Use graphing technology to graph each equation. Describe how each graph changes from the previous graph and draw a sketch of the change.
equation description of change sketch of graph \(y=x^2\) original graph \(y = (x-5)^2\) \(y=(x-5)^2+4\) - Describe the change in the given sketch and write an equation that you think would generate that change.
equation description of change sketch of graph \(y=x^2\) original graph - How would the graph of \(y=\text-2x^2-3\) compare to the graph of \(y=2x^2-3\)?

### 17.3: Select a Function

Let’s call the graph of \(y=x^2\) “the original graph.”

Select the function that will affect the original graph in the way described.

- Shift the vertex of the graph left 1 unit.
- Shift the vertex of the graph up 1 unit.
- Shift the vertex of the graph right 1 unit and up 1 unit.
- Make the original graph narrower.
- Make the original graph narrower, and shift the vertex 1 unit to the right.

- \(y=x^2+1\)
- \(y=(x+1)^2\)
- \(y=3x^2\)
- \(y=(x-1)^2+1\)
- \(y=3(x-1)^2\)