Graphs of simple quadratic relations arising from real-life problems
Name:______________________________
In this activity you will construct relations arising from real-life problems and plot their
corresponding graphs.
1. Open Geometers Sketchpad
2. Click on Graph->Grid Form->Rectangular Grid
Then open the image of Golden Gate Bridge from
Handouts:\Mrs. Sediako\MPM2D\Chapter4\Golden Gate Bridge.png.
Copy and Paste the image to the GSP.
Adjust the position of the bridge with relation to the origin: the origin is at the base if
the South tower of the bridge.
San Francisco Golden Gate Bridge is a suspension bridge over the Golden Gate, a
strait between San Francisco Bay and the Pacific Ocean. It connects the city with
Marin County. The bridge was designed and built in 1929-1937. Irving Morrow acted
as consulting architect and Joseph Strauss was the designer and chief engineer.
Actual construction started in January, 1933.
3. What is the possible shape of the curve of the bridge?
_________________________________
4. The actual length of a central span of the bridge (from South Tower to the North
Tower) 1280 m. Adjust the horizontal scale of the x-axis.
5. The height of the tower above roadway is 152m.
Adjust the vertical scale of the y-axis.
6. Select the Point tool, and moving a cursor along a suspension cable of the bridge
click on the shape marking points.
7. Click Measure -> Coordinates to get the coordinate for the points marked. Write down
the points with their coordinates:
x
y
8. What relation can be used for modelling the shape? _____________________
9. Using the points with their coordinates, find the equation of the graph in vertex form.
Show your steps:
10. What is the equation of the shape of the bridge in standard form?
11. What does x represent? _______________________________________________
12. What does y represent? _______________________________________________
13. Where parabolas may occur in nature? Give several examples with images.
__________________________________
14. Develop the equation for Arc of Costantine in vertex and standard forms.
Image acr.jpg. Use the following dimensions for the scale:
(The People and Senate of Rome
built this arch out of pre-existing
materials in 315 AD for both the
tenth anniversary of the great
emperor, and in honor of his victory
over Maxentius at the battle of
Ponte Milvio in 312.
15. Search the Internet to find parabolic (quadratic) shapes in nature, architecture,
design, decorations, or constructions. Find the equations for the shapes using
GSPprogram.
For each image analyze:
Does the relation have minimum or maximum?
What equation models the shape?
What are the coordinates for vertex of the parabola?
What are the zeros of the parabola?
Write quadratic model in vertex, standard, and factored forms.