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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?

 Jan 15, 2020
 #1
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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 ! 

 Jan 15, 2020

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