Applications of Ouadratic Functions 12.20
1. A manufacturer of fax machines find that the cost(in dollars) generated by manufacturing x units per week is given by the function C(x)=0.15x²-39x+4500. How many units should be manufactured to minimize the cost?
2. The main cable of a suspension bridge has the shape of a parabola. The cables are strung from the tops of two towers, 200 feet apart, each 50 feet high. The cable is 5 feet above the roadway at the point that is directly between the towers. A. Determine a function for the parabola. B. How long is the vertical support cable that is 40 feet from one of the towers?
3. The arch of a doorway is in the shape of a parabola. The bottom of the arch is 4 feet above the floor, and the top of the arch is 8 feet above the floor.The doorway is 4 feet wide A. Determine the function for the parabola. B. Is it possible to pass a box with dimensions 6×3×10 feet through the doorway?
4. What is the greatest area of a pasture in the shape of a rectangle that can be fenced with 6000 feet of fencing?
5. Suppose that f(x)=x²-kx+16. Determine a value for k such that the graph of f
has: A.No x-intercepts. B.Exactly one x-intercept. C.Two x-intercepts.
6. Suppose that f(x)=x²-4x+c. Determine a value for c such that the graph of f has:
A.No x-intercepts. B.Exactly one x-intercept. C.Two x-intercepts.
7. A cylindrical alurninum can is being constructed to have a height h of 4 inches (see figure). If the can is to have a volume of 28 cubic inches, approximate its radiusr