a steel bridge arch is a parabolic in shape. 190m from the base of one leg the arch is 200m high

Question

a steel bridge arch is missouri parabolic in shape. it is 190m from the base of one leg to to the base of the other leg. the arch is 200m high. determine the algebraic expression in standard from, that models the shape.

Answer 1

vertex=(0,200)

x intercepts = (-190,0) and (190)

y= a(x-0)^2+200= ax^2 +200 (in vertex form)

= a(x+190)(x-190) (in x intercept or zero form)

=a(x^2-190^2)= ax^2 -a(36100)

set the constant terms equal

200= -36100a

-36100a=200

a=-200/36100

a=-2/361

y= f(x)= (-2/361)x^2 +200

however the problem seems stated 2 different ways

2nd way has intercepts (190/2,0) and (-190/2,0) = (95,0) and (-95, 0)

if that's the problem, wourk it the same way, but "a" will have a larger absolute value or a smaller negative value, exactly double

a(x^2-9025)=ax^2 +200

a=-200/9025 =-4/361

y=f(x)= (-4/361)x^2 +200

the problem in bold darker script has the 1st solution

lighter smaller script has the 2nd solution, double the 1st