Well here's a parabola that has x-intercepts 0, 12.
y = , you should find 'a' given the height is 18, i.e. use the point (6,18)
What do you get?
What is the maximum height that an 8-foot-wide truck can be in order to pass through a parabolic tunnel that is 18 feet high and 12 feet wide?
I drew the parabola, and tried to find similar triangles, but i didn't notice anything. Any help is appreciated.
Hello, rtblue!
What is the maximum height that an 8-foot-wide truck can be in order
to pass through a parabolic tunnel that is 18 feet high and 12 feet wide?Code:(0,18)| * * | * * | * * | * | * | * | | ----*-------+-------*---- (-6,0) | (6,0) |
The general equation of a parabola is: .
The parabola passes through three points: .
Substitute these coordinates into the equation:
. .
Solve the system of equations: .
Hence, the parabola is: .
The truck is 8 feet wide.
How high is the tunnel at ?
Code:18| * * | * *- - + - -* *| | |* | | | * | | y| * | | | | | | ----*--+----+----+--*---- -6 -4 | 4 6 |
At
Therefore, the truck can be 10 feet high (at most).
thot I would join the party altho the high cards have already been dealt
but...
you could view this as an parabola with axis of symetry on y axis. thus the vertex is and we have another point on the graph of not using the the point
then
vertex or
from the other point we plug in to get
so
so the equation for axis of symmetry over y is
leting then or but this of course actually touches the roof of the tunnel.
Write the equation of your parabola in turning point form...
.
You know the turning point is (since the parabola is symmetrical), and you know that and are points. Substitute into the equation...
.
So the equation of the parabola is .
Your truck is wide, so that means there are on either side. So you want to find the height of your parabola ( value) when or when .