Math 1310 Class Notes – Section 3.5, Page 1 of 6
Math 1310
Section 3.5
Maximum and Minimum Values
Next, we’ll look at a specific type of function, the
quadratic function
.
A
quadratic function
is a function of the form
,
)
(
2
c
bx
ax
x
f
+
+
=
where
a, b
and
c
are
real numbers and
0
≠
a
.
We can write a quadratic function in the form
k
h
x
a
x
f
+

=
2
)
(
)
(
. This is called the standard or vertex form of the quadratic equation.
The graph of a quadratic function is a parabola with vertex
)
,
(
k
h
.
It will open either
upward or downward.
If it opens upward, it has a minimum value
k
.
If it opens
downward, it has a maximum value
k
.
We can use the graph of the quadratic function to
help us find the maximum or minimum value of the function.
Our first task will be to change a given quadratic function from the form
c
bx
ax
x
f
+
+
=
2
)
(
to standard form.
We’ll complete the square to do this.
Once the
function is in standard form, we can sketch a graph using transformations and then read
off the maximum or minimum value.
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 Summer '08
 MARKS
 Real Numbers, Quadratic equation, minimum value

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