Question 204169
Usually  a  quadratic  equation  deals  with  area, length  * width
.
In  this  case  we  could  ask  for  the  area  if  a  rectangle, that  is  similar  to  a  square(x*x),  but  has length longer  by  3,  and  width  shorter  by 5
However,  this  will  result  in a  number,  not  zero
.
If  we  expand  (x+3)(x-5) = x^2 -2x -15 =0,,  and  set  it  equal  to  y, we  have  a  parabolic  function, (y+15) =x^2 -2x,,or (y+15) +1 = x^2 -2x +1,,,,
(y+16) = (x-1)^2
.
We  could  then  ask  for  the  roots  of  the  function.
.
In  real  life  application,  this  could  be  temperature, with  limits at  y=0,,
or  population  trends, with critical points  at  y=0,
or the  definition  of  projectile  motion(football,or  bullet),  and  y=0 would  define  range.