Quadratics Performance Task Math 20-
University Bridge Project NAME: ____________
This task will assess your knowledge of the outcomes you have studied in chapters
3 and 4. You will be assessed on processes not just your answers, so be sure to
communicate how you arrive at your answers.
BACKGROUND INFORMATION
Saskatoon, also known as the "City of Bridges", is located on the banks of the South
Saskatchewan River. The river is crossed by seven bridges within the city limits.
One of those bridges is the University Bridge. Construction on the bridge
commenced in 1913 allowing access to the newly opened university campus. It was
three years later on October 31, 1916 when the bridge was officially opened. The
population at the time, according to a federal census, was 21, 054 people.
By the mid 1960's the population of Saskatoon had grown to over 100 000 people.
To ease the traffic congestion on other roads, an underpass was constructed. The
riverbank under the University Bridge was built up to accommodate the new road.
Did the engineers who designed the underpass in the 60's allow for semi-
trailer traffic?
To help us answer this question a little more information is required.
1. The width of the roadway from the center of the double to the edge of
the road is 29 feet.
2. The gutter of the road extends 13 feet from the outer edge of the road
on either side. The endpoints of the arch begin at the end of the gutter.
3. The center of the arch reaches to a height of 18 feet above the road.
4. The “Trucking Guide to Saskatchewan Weight and Dimension Regulations”
(found on the Saskatchewan Highways and Transportation web site) states
that the legal dimensions for truck width and height are 8.5 feet and 13.5
feet respectively.
Will the semi described above be able to travel under this
underpass?
Quadratics Performance Task Math 20-
1
PART I
The following is a picture of the University Bridge in Saskatoon. Below it, is
a graphical representation of the underpass under the bridge, made by
placing the vertex on the y-axis.
*** ignore the dimensions given in the photo below.
(0, 0)
y
18’
29’
13’
(29, ?)
x
Quadratics Performance Task Math 20-
1
1. What are the coordinates of the vertex of the underpass? ___________
2. Does the arch open up or open down? _________________________
3. Does the arch representing the underpass have a minimum or maximum
value?
_______________________________
4. What is the minimum or maximum value of the underpass? __________
5. How would you be able to tell if the parabola opens up or down if you are
only provided with the equation?
_____________________________________
6. What are the coordinates representing the endpoints of the arch? _____
7. Algebraically determine the function representing the parabolic arch of
the University Bridge underpass in the form y a ( x p ) q . Be sure to
2
prove your “a” value using algebra substitution.
Function: ___________________________
Quadratics Performance Task Math 20-
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PART II
(0, 0)
y
18’
29’
13’
(29, ?)
10. What is the maximum vehicle height that can pass under the arch at the
outer edge of the roadway? Demonstrate your answer algebraically.
x
_____________
11. Is the underpass able to accommodate semi-truck and trailer units?
Explain your answer. Include any limitations that exist for the truck and
trailer units to pass.
Quadratics Performance Task Math 20-
1
________________________________________________________
PART III
1. Another arch of the bridge can be defined by the equation
x 2−168 x+ 98 y+5292=0.
a. Change the equation into vertex form by completing the square.
b. Using the vertex form of the equation you determined above, explain
how the new arch relates to the original arch you determined in Part I
#7.
Quadratics Performance Task Math 20-
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c. City Planners are deciding to hang a banner across the top of the
bridge arch defined by the equation −x 2+ 168 x−5292=0. If they hang
it at a vertical height of 16 ft, algebraically determine where should
they tack the banner on the arch?
