Activity Overview
Eastlands shopping centre is Melbourne’s east is home to beautiful series of parabolic arches. One of the main atriums is lit by vaulted ceilings in the form of parabolas. In this activity students determine the equation to some of these arches and find the variant and invariant properties.
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.