Question

The arch support of a bridge can be modeled by y=-0.00125x^2, where x and y are measured in feet. a) the width of the arch is 800 feet. Describe the domain of the function and explain. Find the height of the arch.

Answer 1

Answer:

The given function is

$y=-0.00125x^{2}$

Which is a parabola concave down with vertex at the origin of the coordinate system.

If the width of the arch is 800 feet, that means 400 feet on negative side and 400 feet and positive.

The image attached shows the graph of this parabola, where you can see the points for each extreme of the arch.

Notice that each point of the base of the arch is at y = -200, that means the height of the arc is 200 feet.

Now, the domain for this function is all real numbers. The range for this function is all number least or equal than zero.

$D: (infinite, -infinite)\\R: [0, -infinite)$