Question 875239
In physics class they teach you that the trajectory of an object is a parabola when
the object is close enough to Earth's surface,
it had some initial horizontal velocity,
and the only force acting on that object is gravity.
 
The path (with x as the horizontal distance and y as the height) looks like this:
{{{graph(300,300,-20,180,-0.1,0.9,-0.00015x^2+0.0225x)}}} {{{y(0)=0}}} and {{{y=150)=0}}}
And, of course, the maximum for {{{y}}} occurs halfway between those two points,
at {{{x=(0+150)/2=75}}} .
At that point, {{{y(75)=100}}} .
As a second degree polynomial function with zeros at {{{x=0}}} and {{{x=150}}} ,
the function can be written, in factored form as
{{{y=K*(x-0)*(x-150)}}} or {{{y(x)=Kx(x-150)}}} .
To find the constant {{{K}}} we use the fact that {{{y(75)=100}}} .
{{{K*75(75-150)=100}}}
{{{K*75(-75)=100}}}
{{{-75^2*K=100}}}
{{{K=-100/75^2}}}
That fraction can be simplified before we start multiplying away.
{{{K=-100/75^2=-4*25/(3*25)^2=-4*25/(3^2*25*2)=-4/(3^2*25)=-4/225}}}
So the equation of the parabola is
{{{y=-(4/225)x(x-150)}}} ---> {{{y=-(4/225)x^2-150(-4/225)x}}} ---> {{{y=-(4/225)x^2+(40/15)x}}} .