Question 826452
The truck travels through a tunnel with a wide opening in the shape of a parabola that is 12 meters wide and and 6 meters high.
:
using the form ax^2 + bx + c = y
Let's have the parabola have the axis of symmetry at 0, then c = 6
and the x intercepts will be -6 and +6 (12 m apart)
write an equation for x = 6, y = 0 and for x = -6, y = 0
36a + 6b + 6 = 0
36a - 6b + 6 = 0
-----------------adding eliminates b, find a
72a + 12 = 0
72a = -12
a = -12/72
a = -.167
The middle term cancels so we can write the equation
T(x) = -.167x^2 + 6
y = -.167x^2 + 6, graphically
{{{ graph( 300, 200, -10, 10, -3, 10,-.167x^2 + 6, 3.3 ) }}}
note that it is 12m wide and 6 m high
:
You can create a table using x and finding y to determine what the height the
truck can be if you know the width of the truck
For example if the truck were 8 ft wide, (x = +4, -4), then
-.167(4^2) + 6 = 3.3 meter, load height has to be less than 3.3 meters (green line)