Chapter 7 Practice Test With Answers - Montville Township Public Schools Page 2
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9Practice Test - Chapter 7
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6.
BRIDGES At 1.7 miles long, San Francisco’s
5.
x = t
– 1 and y = 2t + 1
was the longest suspension
Golden Gate Bridge
SOLUTION:
bridge in the world when it was constructed.
Solve for t.
equation for the design of the bridge.
y
= 2t + 1
y − 1 = 2t
= t
a. Suppose the design of the bridge can be
modeled by a parabola and the lowest point of the
Substitute for t.
2
cable is 15 feet above the road. Write an equation
x
− 1
= t
for the design of the bridge.
x
=
− 1
b. Where is the focus located in relation to the
vertex?
x + 1 =
SOLUTION:
x + 1
a. Since the cable resembles a parabola that opens
=
up, the standard form of the equation that can be
2
4(x + 1) = (y − 1)
2
used to model the cable is (x − h)
= 4p (y − k). If
the parabola is centered on the y–axis, the vertex is
Make a table of values to graph y.
located at the point (0, 15). One point that lies on the
x
y
parabola is (2100, 500).
–1
1
–1, 3
0
Use the values of h, k, x and y to solve for p .
3
–3, 5
2
= 4p (y − k)
(x − h)
8
–5, 7
2
= 4(p )(500 − 15)
(2100 − 0)
4410000 = 1940p
Plot the (x, y) coordinates and connect the points to
2273.2 ≈ p
form a smooth curve.
Use the values of h, k and p to write an equation for
the design of the bridge.
2
= 4p (y − k)
(x − h)
2
= 4(2273.2)(y − 15)
(x − 0)
2
= 9092.8(y − 15)
x
b. The distance between the vertex and the focus is
p. Since p was found in part a. to be 2273.2 feet, the
6.
BRIDGES At 1.7 miles long, San Francisco’s
focus is located 2273.2 feet above the vertex.
was the longest suspension
Golden Gate Bridge
bridge in the world when it was constructed.
Write an equation for the hyperbola with the
given characteristics.
equation for the design of the bridge.
7.
vertices (3, 0), (–3, 0); asymptotes
SOLUTION:
Because the y–coordinates of the vertices are the
a. Suppose the design of the bridge can be
same, the transverse axis is horizontal, and the
modeled by a parabola and the lowest point of the
cable is 15 feet above the road. Write an equation
–
standard form of the equation is
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for the design of the bridge.
Page 2
b. Where is the focus located in relation to the
vertex?
= 1.
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