Question

Question 6Points 3The Gateway Arch in a city has the shape of a catenary (a U-shaped curve similar to aparabola). It can be approximated by the following model, where x and y aremeasured in feet.y=-(3/1000)x + 400)x - 400). How high is the arch?

Answer 1

Step-by-step explanation:

The model is given below as

`=-(3)/(1000)(x+400)(x-400)`

To figure out the value of the height of the we will expand the brackets

`\begin{gathered} -(3)/(1000)(x+400)(x-400) \\ =-(3)/(1000)(x^2-160000) \end{gathered}`

With no x-term, the vertex is at x=0

Substitute x=0,to get y

`\begin{gathered} =-(3)/(1000)(0-160000) \\ =-(3)/(1000)*-160000 \\ =480feet \end{gathered}`

Using the graphical method, we will have

Hence,

The final answer is

`\Rightarrow480feet`