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...

The standard form of a parabola is class="AM">`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:

class="AM">`y=a(x-0)^2+26`

class="AM">`0=a(21)^2+26`

class="AM">`-26=441a`

class="AM">`a=-26/441`

class="AM">`y=-26/441(x)^2+26`

Here is the
graph:

src="/jax/includes/tinymce/jscripts/tiny_mce/plugins/asciisvg/js/d.svg"
sscr="-30,30,-10,30,10,10,1,10,10,300,200,func,-26/441*x^2+26,null,0,0,-21,21,black,1,none"/>

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