Quadratic Functions: A bridge with a parabolic arch goes over a river....

[allae]

A bridge with a parabolic arch goes over a river. The shape of the arch can be modeled by the function h = -1/4w^2 + 4w, where h represents height in meters and w represents width in meters.
a) What is the maximum height of the arch?

b) How wide is the bridge?

c) a sailboat floats directly down the middle of the river. If its square sail sits 14 m above the top of the water and is 6 m wide, will it be able to sail under the bridge?

 

[Deleted member 4993]

A bridge with a parabolic arch goes over a river. The shape of the arch can be modeled by the function h = -1/4w^2 + 4w, where h represents height in meters and w represents width in meters.
a) What is the maximum height of the arch?

b) How wide is the bridge?

c) a sailboat floats directly down the middle of the river. If its square sail sits 14 m above the top of the water and is 6 m wide, will it be able to sail under the bridge?

What are your thoughts?

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[stapel]

A bridge with a parabolic arch goes over a river. The shape of the arch can be modeled by the function h = -1/4w^2 + 4w, where h represents height in meters and w represents width in meters.

a) What is the maximum height of the arch?

They've given you a negative quadratic, which you know (from experience with graphing) creates an upside-down parabola. You've been asked to find the maximum height of that parabola, which you know means finding the vertex. Where are you stuck in the process?

b) How wide is the bridge?

You know the value that h must take on at "ground level". You plugged this value in for h and solved the quadratic, perhaps by using the Quadratic Formula. You subtracted the two values and... then what?

c) a sailboat floats directly down the middle of the river. If its square sail sits 14 m above the top of the water and is 6 m wide, will it be able to sail under the bridge?

What is the width at h = 14?