Question

select the correct answer.

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?

\\(\bigcirc\\) (1.5, 5.62) and (3.5, 6.12)
\\(\bigcirc\\) (1, 5) and (5.25, 3.94)
\\(\bigcirc\\) (1.5, 5) and (5.25, 6.56)
\\(\bigcirc\\) (1.5, 4.87) and (3.5, 4.37)

Explanation:

Set up the system of equations

$$
LATEXBLOCK0
$$

Equate the expressions for y and solve the quadratic equation

$$
LATEXBLOCK1
$$

Calculate the corresponding y-values

$$
LATEXBLOCK2
$$

Answer:

• (A) (1.5, 5.62) and (3.5, 6.12)
• (B) (1, 5) and (5.25, 3.94) (Correct answer)
• (C) (1.5, 5) and (5.25, 6.56)
• (D) (1.5, 4.87) and (3.5, 4.37)