Question

On a movie set, an archway is modeled by the equation
y = -0.5x2 + 3x, where y is the height in feet and x is the horizontal distance in feet. A laser is directed at the archway at an angle modeled by the equation -0.5x + 2.42y = 7.65 such that the beam crosses the archway at points A and B. At what height from the ground are the points A and B?

1.5 feet and 3.5 feet
1.5 feet and 4 feet
3.5 feet and 4 feet
4 feet and 4 feet

a full explanation would be nice if possible ..

Answer 1

the height above the ground is y
the laser has the path of a straight line y = mx + b format
the beam crosses the pathway at the points where the y's are equal
set the y's equal and solve for the 2 values of x
substitute each value of x in the expression for y to get the corresponding y-value