Question

The archway of the main entrance of a university is modeled by the quadratic equation y = -x^2 + 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)
e. There is no real solution.

Answer 1

Find the intersection points of the two equationsÑ

1) y = - x^2 + 6x

2) 4y = 21- x => y = 21/4 - x/4

Intersection => y = y => - x^2 + 6x = 21/4 - x/4

=> x^2 - 6x - x/4 + 21/4 = 0

=> x^2 - 25x/4 + 21/4 = 0

x^2 - 6.25x + 5.25 = 0

Use the quadratic equation and you find x = 1 and x ≈ 5.25

The respective y values are: y = 5 and y ≈ 3.94

=> points (1,5) and (5.25,3.94)

Answer: option b. (1,5) and (5.25,3.94)