Question

A rain gutter is made from aluminum sheets that

28 cm wide. The first step in forming a rain gutter is to lift the edges of the aluminum sheet to form right angles, as show in in the illustration below. The cross-section
area formed by the raised edges affects the water flow. This cross-section area, A, can be represented by the function A = x(28-2x) where x
represents the height of the raised edges.
1. To the nearest centimetre, determine the height of the raised edge, x cm, which will maximize the
transverse area.

Answer 1

7 cm

Explanation:

For any quadratic function f(x)=ax²+bx+c given in form f(x)=a(x-h)²+k, where:

h=-b/2a and k=f(h) the point (h, k) is vertex of the function graph.

It means that k is maximum (if a<0) or minimum (if a>0) value of function and x=h is the x which will maximize function.

A(x) = x(28-2x) = 28x - 2x² = - 2x² + 28x ⇒ a = -2 , b = 28

h = -28/[2•(-2)] = 7