Question 184046: The arch of a bridge is in the shape of a parabola and is 14ft high at the center and 20ft wide at the base.
a.) What is the tallest 8ft wide truck that can pass through the arch?
b.) what is the widest 12ft high truck that can pass through the arch?
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! I would plot the parabola and put one x-intercept at the origin
(0,0) and the other x-intercept at (20,0). That would put the
y-intercept at the origin.
The general equation is
I have to find a, b, and c
since one intercept is at (0,0), I can say
And the other x-intercept is at (20,0)
The arch is 14 ft high at the center
This is the vertex. The x-value of the vertex is
This is the x-coordinate of the vertex
The problem says  at the vertex
so, (10,14) is a point on the curve
From above,
and
The equation is
I'll plot it
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a.) What is the tallest 8ft wide truck that can pass through the arch?
If it goes straight down the middle, it will cover 4 ft on either side
The center of the arch is at  . 4 on either side would
be  and  . I should get the same y-value
for both of these
The tallest truck is 11.76 ft tall
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b.) what is the widest 12ft high truck that can pass through the arch?
It is 6 ft on either side of
I can use either one to find 
The tallest truck is 8.96 ft tall
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