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? 

A

Two triangles in an x y plane.

B

Two triangles in an x y plane.

C

Two triangles in an x y plane.

D

Two triangles in an x y plane.

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
    Parabola in the x y plane.
    \(y = (x-5)^2\)  
    Parabola in the x y plane.
    \(y=(x-5)^2+4\)  
    Parabola in the x y plane.
  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
    Parabola in the x y plane.
       
    Two parabolas in the x y plane.
       
    Three parabolas in the x y plane.
  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.
  • \(y=x^2+1\)
  • \(y=(x+1)^2\)
  • \(y=3x^2\)
  • \(y=(x-1)^2+1\)
  • \(y=3(x-1)^2\)

Summary