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Lecture 13: Section 2.1
Quadratic Functions and Models
Def.
A
quadratic function
is a second degree
polynomial of the form
f
(
x
) =
ax
2
+
bx
+
c
where
a; b
and
c
are real numbers and
a
6
= 0.
NOTE:
The graph of a quadratic function is a
transformation of the parent function
f
(
x
) =
x
2
. Its
graph is in the shape of ’U’ called a
parabola
.
ex.
Graph
f
(
x
) =
±
(
x
±
3)
2
+ 2
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View Full Document Standard form of a quadratic function
The quadratic function can be written in
standard
form
f
(
x
) =
a
(
x
±
h
)
2
+
k;
a
6
= 0
The standard form is convenient for sketching:
1.
Vertex:
2.
Axis of Symmetry:
All parabolas are symmetric with respect to a line
called
axis of symmetry
.
3. Parabola opens
upward
if
;
The vertex (
h; k
) is the
point.
Parabola opens
downward
if
;
The vertex (
h; k
) is the
point.
4. The graph is a transformation of
f
(
x
) =
x
2
.
If
j
a
j
>
1, the graph is
stretched vertically
and if
0
<
j
a
j
<
1, the graph is
compressed vertically
.
To write a quadratic function in standard form, we
complete the square
.
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This note was uploaded on 07/08/2011 for the course MAC 1140 taught by Professor Williamson during the Spring '08 term at University of Florida.
 Spring '08
 WILLIAMSON
 Calculus, Algebra

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