# 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

1. 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 $$y = (x-5)^2$$ $$y=(x-5)^2+4$$ 2. 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 3. 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.

1. Shift the vertex of the graph left 1 unit.
2. Shift the vertex of the graph up 1 unit.
3. Shift the vertex of the graph right 1 unit and up 1 unit.
4. Make the original graph narrower.
5. Make the original graph narrower, and shift the vertex 1 unit to the right.
• $$y=x^2+1$$
• $$y=(x+1)^2$$
• $$y=3x^2$$
• $$y=(x-1)^2+1$$
• $$y=3(x-1)^2$$