Is "y=-0.00635x^2+4.0005x" in the correct form to be a parabola

Yes.

Any parabola is represented by an appropriate second degree polynomial, which means that to identify a particular parabola you have to choose three coefficients to identify the polynomial

In your case, the expression comes from the choice , and so by all means its graph is a parabola.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.