Question 888333
Working from standard form will be easier.


The road being 20 m wide means that half-way from the origin  is  10 m, the "x" value for the vertex.  The y value for the highest point is 19 m.  The vertex is therefore (10,19).


Equation is {{{y=a(x-10)^2+19}}}.  You also are given as instruced in part (a) that (0,0) is one of the points.  This means {{{0=a(0-10)^2+19}}}
{{{100a=-19}}}
{{{a=-(19/100)}}}.


The equation fully in standard form is {{{highlight(y=-(19/100)(x-10)^2+19)}}}.