Answer :
Answer:
[tex]y=-\frac{1}{100}(x-50)^2+25[/tex]
the height of the arch 10 feet from the center is 24 feet
Step-by-step explanation:
An arch is in the shape of a parabola. It has a span of 100 feet, the vertex lies at the center 50 and the maximum height of 25 ft.
Vertex at (50,25)
vertex form of the equation is
[tex]y=a(x-h)^2+k[/tex], (h,k) is the center
[tex]y=a(x-50)^2+25[/tex]
the parabola starts at (0,0) that is (x,y)
[tex]0=a(0-50)^2+25[/tex]
subtract 25 from both sides
[tex]-25=a(-50)^2[/tex]
[tex]-25=a(2500)[/tex]
divide both sides by 2500
[tex]a=-\frac{1}{100}[/tex]
[tex]y=-\frac{1}{100}(x-50)^2+25[/tex]
the height of the arch 10 feet from the center.
center is at 50, 10 feet from the center so x=40 and x=60
[tex]y=-\frac{1}{100}(40-50)^2+25[/tex]
y=24
the height of the arch 10 feet from the center is 24 feet