1. Determine the nature of the quadratic functions with formula:

2. Given the quadratic function y = f (x) = 2x² −11x +12 Decide whether the graph of f(x) has a minimum or a maximum value, and evaluate it.

3. A gun is situated at a point O on horizontal ground at sea level. It fires a shell which reaches a maximum height of 1000 m and lands at A, also at sea level, a horizontal distance of 10 km from O. The path of the shell is a parabola. Choosing suitable units, sketch the path (vertical height against horizontal distance), and show that an appropriate function f₁(x) to describe it is

where O is the origin of co-ordinates and x is the horizontal distance covered. The gun is transported to a point P at the top of a mountain 960 m above sea level, and fired in an identical manner. The shell lands at a point B at sea level. Sketch this path, derive a second function 2f(x) to describe it, and show that

Deduce the horizontal distance of B from P.

4. An agent for a block of 50 flats knows that he can just fill all the flats if he charges a rent of £240 per month. From experience, he knows that for each increase of £6 per month, one flat becomes vacant.

(a) Sketch a graph of I against x.

(b) How many flats should be left vacant for maximum income, and what rent should be charged?

(c) The agent discovers that the cost of maintaining an occupied flat is £140 per month, whereas an unoccupied flat costs only £80 per month. Show that the monthly profit P is given by

Find the number of flats occupied for maximum profit.

Transcribed Image Text:

(a) y = x-3x-28 (c) y = 2x -5x+13 (e) y = 1+x(2-3x) (b) y = x - 7x (d) y = 5x-7-x (f) y = 4x - 4x+1