Answer
a) maximum
b) 2035
c) 311 million phones
Work Step by Step
a)
The coefficient of the $x^2$ term is negative, so the graph opens down. Since the graph opens down, the vertex of the graph is the graph’s maximum point.
b)
$c(x)=-.4x^2+21x+35$
The highest (or lowest) point on a graph is found using the vertex of a graph. The vertex of the graph has the equation $x=-b/2a$.
$a=-.4$, $b=21$, $c=35$
$x=-b/2a$
$x=-21/2*-.4$
$x=-21/-.8$
$x=21/.8$
$x=26.25$
Rounded to the nearest year, $x=26$
$26+2009=2035$
c)
$c(x)=-.4x^2+21x+35$
$c(26)=-.4*26^2+21*26+35$
$c(26)=-.4*676+546+35$
$c(26)=-270.4+581$
$c(26)=310.6$
