Algebra one

Question

A fountain on a lake sprays water in a parabolic arch modeled by the equation y = -0.3x^2 + 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?

Answer 1

Hi Saralyn,

 

Solve for y in the second equation and set it equal to the first to find the point of intersection of x = 7.13. Substitute this value into either of the two original equations to find the value of y as 6.14.  OR

 

Graph both equations on a graphing calculator to find the point of intersection and note the value of the y coordinate.