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?
A(1, 5.5) and (5.25, 6.56)
B(1, 5) and (5.25, 3.94)
C(1.5, 4.87) and (3.5, 4.37)
D(1.5, 5.62) and (3.5, 6.12)
EThere is no real solution.

Answer 1

Basically look for the intersection points of these two functions by setting them equal to each other.

-x^2 + 6x = 21/4 - x/4

-x^2 + (25/4)x - 21/4 = 0

x = 1 and x = 21/4

Plug these points back to any of the two original equations, you will get

(1,5) and (21/4, 63/16)

Answer 2

1.5 ........ 5.25..... 3.94