The surface of a pedestrian bridge forms a parabola. Let the surface at one side of the bridge be represented by (6, 0) and the surface at the other side be represented by (14, 0). The center of the bridge is 2 feet higher than each side and can be represented by a vertex of (10, 2). Write a function in vertex form that models the surface of the bridge. Can you also check my profile and answer my other question its worth 100 points

y = -1/8(x - 10)^2 + 2

Step-by-step explanation:

the word problem tells you that the X-intercepts are (6, 0) and (14, 0)

the vertex is (10,2)

vertex form is y=a(x-h)^2+k with (h,k) being the vertex

so just plug in the vertex and one of the points (an x intercept will work)

y = a(x - h)^2 + k

0 = a(6 - 10)^2 + 2

simplify:

-2 = a(6 - 10)^2

-2 = a(-4)^2

-2 = 16a

-2/16 = a

-1/8 = a

y = -1/8(x - 10)^2 + 2

Step-by-step explanation:

The surface of a pedestrian bridge forms a parabola. Let the surface at one side of the bridge be represented by (6, 0) and the surface at the other side be represented by (14, 0). The center of the bridge is 2 feet higher than each side and can be represented by a vertex of (10, 2). Write a function in vertex form that models the surface of the bridge.

Can you also check my profile and answer my other question its worth 100 points

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,