Question 134020
{{{h=.043d^2+2.365d}}}


Maximum height is at the vertex.  For a parabola {{{y=f(x)=ax^2+bx+c}}}, the vertex is located at ({{{-b/2a}}},{{{f(-b/2a)}}}).  For your equation, d is the independent variable, so a = .043 and b = 2.365.


{{{-b/2a=-2.365/2(.043)=27.5}}} and {{{f(-b/2a)=f(27.5)=.043(27.5)^2+2.365(27.5)=97.556}}}


Therefore maximum height is 97.556 feet.


The base is the horizontal axis, so the parabola intersects the base at the roots of {{{.043d^2+2.365d=0}}}.


Factoring:  {{{d(.043d+2.365)=0}}}


Hence {{{d=0}}} or {{{.043d+2.365=0}}} => {{{d=55}}}, so the coordinates of the intersection of the parabola with the base on the d-h plane are (0,0) and (55,0).


The distance between two points on a horizontal line is the difference between their x (rather d, in this example) coordinates.  {{{55-0=55}}}