Math Concepts and Examples

Topic : parabola

Question : Growth rate y (in pounds/month)of an infant is related to the present weight x(in pounds)by formula y= cx(21-x)where c is a positive constant.0<x<21.At what rate does the maximum growth occur.

Answer :

The y coordinate of the vertex is the max of a quadratic if the parabola is downward and its the minimum if its upward.

the parabola is upward if the co efficient of x^2 is positive and downward if its negative.

here we have y= c x(21-x)= 21cx -c x^2

as the co efficient of x^2 is negative, we get a maximum value

formula: for y = ax^2+bx+c , the vertex is given by ( -b/2a , f( -b/2a) )

hence the maximum y value is -b/2a

here the max growth rate = – 21c / -2c = 21/2 =10.5pounds/month.