quadratic models are bad

Question

A piece of wire of length 14 cm is to be formed into the shape of a rectangle. The length of the rectangle

is x cm.

a Find the width of the rectangle in terms of x.

b Find the area of the rectangle, A, in terms of x.

c Sketch the graph of A versus x

d Find the maximum area of the rectangle and the value of x for which the area is a maximum.

Answer 1

14=perimeter=2w+2x

7=w+x

w(x)=7-x cm= width

A(x)= x(7-x)= -x^2 +7x cm^2 =Area

A(x) is an downward opening parabola

axis of symmetry x=3.5

vertex (3.5, 12.25)= maximum

x intercepts = 0 and 7

y intercept = 0

max Area =(14/4)^2= 3.5^2 = 12.25 cm^2

when x = 3.5 cm

3.5 cm long by 3.5 cm wide, a square