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?

Check the picture below, so, what is from the A coordinates, what's the y-coordinate then.

well, we can get that off either equation, if we just know A coordinates, so let's see what "x" is at those A and B points.





so, as you can see, clearly 6.14 is higher, and thus is B.

thus A is 4.15, so the y-coordinate for point A is 4.15, and that's the distance from the beam hitting the fountain at A, to the ground.