Question

The archway of the main entrance of a university is modeled by the quadratic equation y = -x2 + 6x. The university is hanging a banner at the main entrance at an angle defined by the equation 4y = 21 − x. At what points should the banner be attached to the archway?

Answer 1

Answer:

The point at which the banner should be attached to the archway is going to be given by the point(s) at which the two equations intercept:

y = -x^2 + 6x and 4y = 21 − x

Solving the system of equations, we find that they intercept at: (1, 5) and (5.25, 3.938)

Therefore, the banner should be attached to the archway at the points (1, 5) and (5.25, 3.938)