TEACHER NOTESSummary• Students build a model of a

suspension bridge using corkboard, a chain and weights. Then find the key features and write equations in standard form.

Supplies for each team:• Large sheet of corkboard with

grid• 16-24 inches of chain• weights – paper clips with

washers

Language:• parabola• vertex• maximum or minimum• line of symmetry• orientation• roots• intercepts• quadratic function• quadratic function in

standard form • vertex form

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Build a Bridge

PA.2 Graphing Parabolas

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Math Practice

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Math Practice

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Learning TargetsA-REIc I can represent and

solve equations and inequalities graphically.

Understand and verify that every point (x, y) on the line is a solution to the quadratic equation.

FIFc I can analyze functions using different representations

Find vertex, maximum, minimum, orientation, roots, and intercepts of a parabola.

F-IFb I can interpret functions that arise in applications in terms of the context.

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; relative maximums and minimums; symmetries (origin, x-axis, y-axis); end behavior.

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LAUNCH• Watch this video

https://www.youtube.com/watch?v=xox9BVSu7Ok

Creative Commons License The St. Johns Bridge in Portland Oregon by Cacophony is licensed under a Creative Commons Attribution 4.0 International License.

St. John’s Bridge

Why would I show you this picture?

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Suspension Bridge• The suspension bridge has a parabolic shape. • The parabolic shape allows for the forces of

compression to be transferred to the towers, which upholds the weight of the traffic.

• In a suspension bridge, the roadway is actually hanging from large cables. The cables run over the top of two large towers (which are rooted deep into the earth) and connect to anchorages at each end of the bridge.

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Build your BridgeYou will make a model of the center part of the

bridge with• cork board with a grid on it• 1 chain hung from the origin and x-axis• 5 – 11 evenly spaced

weights

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Creative Commons License - Suspension Bridge by Matthias079 is licensed under a Creative Commons Attribution 4.0 International License

Build your Bridge

Find1. The roots: (0, 0) & (d, 0)2. The line of symmetry.3. The vertex: (x, y)4. The orientation.

5. The equation modeled by your chain.

Use quadratic regression OrUse ax(x – d) = y with

the vertex and roots to find a.

Write your equation in standard form.

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A Challenge – Write your Equation in Vertex Form

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Build your BridgeUse the weights on your chain to find points that

lie on your parabola.Verify these points with the equation(s) you

found.

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©Evergreen Public Schools 2010 13

Debrief• How is this parabola similar to

the ones you saw in the previous section?

• How is it different?