SOLUTION: The New River Gorge Bridge in West Virginia is the second longest steel arch bridge in the world. Its height above the ground, in feet, at a point x feet from the arch's center is

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The New River Gorge Bridge in West Virginia is the second longest steel arch bridge in the world. Its height above the ground, in feet, at a point x feet from the arch's center is       Log On


   

Question 1029552: The New River Gorge Bridge in West Virginia is the second longest steel arch bridge in the world. Its height above the ground, in feet, at a point x feet from the arch's center is h%28x%29=-0.00121246x%5E2%2B876
(a) What is the height of the top of the arch?
The height of the arch is ____ feet.
(b) What is the span of the arch at a height of 525 feet above the ground?
Round your answer to the nearest integer.
The span of the arch is ____ feet.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The general form is:
+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
The given equation is:
+h%28x%29+=+-.00121246%2Ax%5E2+%2B+876+
+a+=+-.00121246+
+b+=+0+
+c+=+876+
---------------
(a)
The formula for the x-value of the vertex is:
+x%5Bv%5D+=+-b%2F%282a%29+
+x%5Bv%5D+=+0+
If you plug this back into the given equation,
you get
+h%280%29+=+-.00121246%2A0%5E2+%2B+876+
+h%280%29+=+876+, the height at the top of the arch
---------------
(b)
Given: +h%28x%29+=+525+
+h%28x%29+=+-.00121246%2Ax%5E2+%2B+876+
+525+=+-.00121246%2Ax%5E2+%2B+876+
+.00121246%2Ax%5E2+=+876+-+525+
+.00121246%2Ax%5E2+=351+
+x%5E2+=+289494.0864+
+x+=+538.05+
and
+x+=+-538.05+
The span of the arch at +h%28x%29+=+525+ is
+2%2A538+=+1076+
1,076 ft span
---------------
Here's the plot of the arch:
+graph%28+800%2C+400%2C+-1000%2C+1000%2C+-100%2C+1000%2C+-.00121246%2Ax%5E2+%2B+876+%29+