.
find the equation of the parabola determined by the given condition:
axis vertical and passing through (0,0), (1,0), and (5,-20).
~~~~~~~~~~~~~~
From the condition, you see that the quadratic polynomial has zeroes at x= 0 and x= 1.
It means that the quadratic polynomial has this factored form
y(x) = ax*(x-1),
where "a" is an unknown coefficient.
To find this coefficient, use the third point, which says that y(5) = -20
a*5*(5-1) = -20,
or
20a = -20,
which gives a = -20/20 = -1.
So, the sough function (polynomial) is y(x) = -x*(x-1) = -x^2 + x. ANSWER
Solved.