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MA 15200
Lesson 37, Sections 3.1 and Appexdix H
If a parabola opens downward, the vertex is the highest point of the graph.
The
y

coordinate of that vertex is the largest value in the range of the function.
That
y

coordinate value is called the
maximum
of the function or equation and that maximum
occurs when
x
=
h
.
There are several real life applications where a maximum value can
be found by writing an equation for a parabola and finding its vertex.
It is important when solving these applied problems that you understand what
‘label’ the
h
and the
k
of the vertex represent.
Examine the following quadratic
functions.
2
( )
0.02
4
12
P x
x
x
= 
+
+
Each ordered pair is of the form
( , )
x P
or (# items, profit)
The above function represents profit for a week based on the number of items
x
made and
sold.
After the vertex
( , )
h k
is found, the
h
represents the number of item made and sold
to get a maximum profit.
The
k
is that maximum profit.
2
( )
2
650
A w
w
w
= 
+
and
650
2
L
w
=

Each ordered pair is of the form
( , )
w A
or
(width, area).
The above function represents the area of a rectangular region where
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This document was uploaded on 01/23/2012.
 Spring '09

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