As a decoration for a school dance, the student council creates a parabolic arch with balloons attached to it for students to walk through as they enter the dance. The shape of the arch is modeled by the equation
y = x(5 – x), where x and y are measured in feet and
where the origin is at one end of the arch. Can a student who is 6 feet 6 inches tall walk through the arch without ducking?
+36916 y = -x^2 + 5x max point will be - b/2a
-5/(-2) = 2.5 this is the value of 'x' at the high point (y)
y high point = - (2.5)^2 +5(2.5) = - 6.25 + 12.5 = 6.25 ft = 6 ft 3 inches DUCK !
