Question

An arch is in the shape of a parabola. It has a span of 100 feet and a maximum height of 25 ft.

Answer 1

Answer:

$y=-\frac{1}{100}(x-50)^2+25$

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

$y=a(x-h)^2+k$, (h,k) is the center

$y=a(x-50)^2+25$

the parabola starts at (0,0) that is (x,y)

$0=a(0-50)^2+25$

subtract 25 from both sides

$-25=a(-50)^2$

$-25=a(2500)$

divide both sides by 2500

$a=-\frac{1}{100}$

$y=-\frac{1}{100}(x-50)^2+25$

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

$y=-\frac{1}{100}(40-50)^2+25$

y=24

the height of the arch 10 feet from the center is 24 feet