Objectives
Students use x and y intercepts to determine an equation for each arch, but what happens when you can’t see one of the y intercepts? The equations are used to make predictions and also to observe the unchanging nature of the dilation factor through the viewer’s perspective.
Vocabulary
- Axis intercepts
- Factors
- Dilation
- Modelling
About the Lesson
Each parabolic arch in the image is modelled by an equation of the form y = a(x-m)(x-n). A point is located on the x axis to help determine the x axis intercepts and similarly on the y axis. When the y intercept is not visible, students are then forced to determine the dilation factor by alternative means. Students also note the invariance of the dilation factor regardless of the perspective.