Imagine you are set designer for Universal Studios movie company. You plan movie sets using freehand sketches and your computer. In one scene, a banner will hang across a parabolic archway. To make it look interesting, you have decided to put the banner at an angle along a line defined by the linear equation y = 0.24x+ 7.2, with x representing the horizontal distance and y the vertical distance in metres, from the foot of the archway. The archway is modelled by the quadratic equation y = - 0.48x2+ 4.8x.

Question

Imagine you are set designer for Universal Studios movie company. You plan movie sets using freehand sketches and your computer. In one scene, a banner will hang across a parabolic archway. To make it look interesting, you have decided to put the banner at an angle along a line defined by the linear equation y = 0.24x+ 7.2, with x representing the horizontal distance and y the vertical distance in metres, from the foot of the archway. The archway is modelled by the quadratic equation y = - 0.48x2+ 4.8x.
a) How can you use the equations to determine the points where the banner needs to be attached to the archway? You can use Technology or the grid below to help with your explanation.
b) What would be the length of the banner? (Show your work)

oobleck · Answer

(a) just set the two functions equal to each other, and solve for x. 0.24x+ 7.2 = - 0.48x2+ 4.8x once you have x, evaluate y at each point. (b) just use your usual distance formula between two points.