Afountain on a lake sprays water in a parabolic arch modeled by the equation  y  = -0.3x2  + 3x.  a beam of light modeled by the equation  -2x  + 5.5y  = 19.5  passes through the fountain to create a rainbow effect.  if the beam cuts the water spray at points a and b, such that point b is at a higher level than point a, what distance from the ground level is point a?

See the attached figure.

Water model ⇒⇒⇒ y = -0.3 x² + 3x        ( blue graph )
Light model   ⇒⇒⇒ -2x + 5.5 y = 19.5    ( red graph )
The intersection between the two models A and B
A = ( 1.657 , 4.148 )
B = ( 7.13 , 6.138 )

B is at a higher level than point A

The distance from the ground level to point A = y-coordinate of point A
                                                                        = 4.148

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