SOLUTION: An engineer is designing a parabolic arch. The arch must be 15 m high and 6 m wide at a height of 8 m. a) Determine the quadratic function b) what is the width of the arch at its b
Question 701375: An engineer is designing a parabolic arch. The arch must be 15 m high and 6 m wide at a height of 8 m. a) Determine the quadratic function b) what is the width of the arch at its base. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! An engineer is designing a parabolic arch.
The arch must be 15 m high and 6 m wide at a height of 8 m.
a) Determine the quadratic function
:
Using the form ax^2 + bx + c = 0
From the information given we can find a, b, c
Let it be centered at 0 so the max height of the arc: x=0; y=15; then c = 15
Two given coordinates
x=-3, y=8
-3^2a - 3b + 15 = 8
x=+3, y=8
3^2a + 3b + 15 = 8
:
Add the two equations
9a - 3b + 15 = 8
9a + 3b + 15 = 8
--------------------addition eliminates b, find a
18a + 30 = 16
18a = 16 - 30
18a = -14
a = -14/18
a = -.78
:
Find b
9(-.78) + 3b + 15 = 8
-7+ 3b = 8 - 15
3b = -7 + 7
3b = 0
b = 0; there is no b
therefore:
The quadratic equation for the arch: f(x) = -.78x^2 + 15
looks like this, green horizontal line at 8 meters,
you can see the width at that point is 6m
:
b) what is the width of the arch at its base.
Find the value of x when y = 0
-.78x^2 = -15
x^2 = -15/-.78
x^2 = +19.2859
x = +/-
x = +4.39
and
x = -4.39
therefore
2(4.39) = 8.78 meters wide
