AChor/MCF3M
Name: _______________________
Date: ________________________
Worksheet 2-10: Applications of Quadratic Functions
1. Marcus is investigating the design of the St. Louis Gateway Arch. It is in
the shape of a catenary, which is similar to a parabola. The function
3
h( x )  
( x  96)( x  96) gives an approximate model for the arch.
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Variable h is the height, in metres, of a point along the arch, and x is the
horizontal displacement, in metres, from the vertex.
(a) What are the zeros of this quadratic function? Explain their significance.
(b) Write the function in standard form.
(c) Find the coordinates of the vertex. Explain their significance.
Assigned Work: WS 2-10; Textbook p. 112 #3, #6, #9, #10
AChor/MCF3M
Name: _______________________
Date: ________________________
WS 2-10
2. Marcus is investigating a parabolic bridge that spans a 40cm wide canal. The equation of the parabolic arch is
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h   x ( x  40) , where x is the horizontal distance from
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the left bank, in metres, and h is the height above water
level, in metres.
(a) What are the zeros of this quadratic function? What is their significance in this situation?
(b) Find the coordinates of the vertex. Explain what these coordinates mean with respect to the bridge.
3. A stone is tossed from a bridge. Its height as a function of time is given by h(t )  5t 2  5t  60 ,
where t is the time, in seconds, and h(t ) is the height of the stone above the ground, in metres, at
time t. How long does it take the coin to reach the ground?
Answers: 1. (a)  96 and 96, the arch is 192 m wide spaced evenly on either side of the vertex
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x  192 , (b) (0, 192), the height of the arch at its midpoint is 192 m;
(b) h ( x )  
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2. (a) 0 and 40, the river is 40 m wide with a value of 0 assigned to the left bank,
(b) (20, 16), the arch has a height of 16 m above the water at the point halfway across the river;
3. 4 s ( t  3 is inadmissible since t  0 and h  0