Bridges often have probolic curve. If the anchors at either end of a bridge are 42 m apart, and the max. height of the bridge is 26m. Find an equationFind an equation that models the shape of the...

Bridges often have probolic curve. If the anchors at either end of a bridge are 42 m apart, and the max. height of the bridge is 26m. Find an equation

Find an equation that models the shape of the bridge.

taylormath | Certified Educator

The standard form of a parabola is `y=ax^2+bx+c` . That is usually the end result for a parabola equation, but rarely will you start with that form. One starting equation for a parabola is the vertex form, `y=a(x-h)^2+k` ,where a is the size/direction factor and (h,k) is the vertex. In the bridge problem, the vertex can be placed at (0, 26) and one of the points is (21,0).  The point is needed to substitute into the equation to find the value of a. The equation takes the form:

`y=a(x-0)^2+26`

`0=a(21)^2+26`

`-26=441a`

`a=-26/441`

`y=-26/441(x)^2+26`

Here is the graph:

This is just one example of the many equations possible to represent the bridge.