1
Summer Lesson 26
MA 152, Section 3.1
I
Quadratic Functions
A
quadratic function
of the form
c
bx
ax
y
+
+
=
2
,
where
a, b,
and
c
are real numbers
(general form)
has the shape of a
parabola
when graphed.
The parabola will open
upward
if the value of
a
is positive and downward is it is negative.
The
vertex
is the
point or ordered pair where the parabola 'turns'.
Ex 1:
Graph the parabola
2
3
2
1
2
+
−
−
=
x
x
y
.
Find its vertex and direction of opening.
We will use a table of values and plot the points.
x
y
0
3/2
1
0
1
2
2
5/2
2
3/2
3
0
This method is tedious.
It will be easier to know how to find the vertex.
We could also
find intercepts and use symmetry.
Notice, the graph is symmetric about a vertical line
through the vertex.
The
vertex
will be an ordered pair (
h, k
).
The
axis of symmetry
is a vertical line with through the vertex.
Points have symmetry
(equal distance) left and right about this vertical line.
The equation will be
x
h
=
.
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 Summer '09
 Real Numbers, Standard form, Quadratic equation, Vertex

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