Algebra I Module 8 Axis of Symmetry Tutorial 2013
This tutorial will guide you throughthe process of understanding whatthe "Axis of Symmetry" is for a parabolaand how to write an equation for it in theform of "x=h".
The axis of symmetry is a vertical line that splitsa parabola into two equal halves.  It is a line thata parabola can be reflected over creating itsmirror image.
Axis of
Symmetry
Vertex
(0,0)
Example:
Axis of
symmetry
Vertex
(2,4)
To write the equation for the "axis of symmetry",one needs only to indentify the "x" componentof the vertex.  This defines the equation for the"axis of symmetry."  This "x" value for the vertexis the "h" value in x = h.
You can identify the "x" component either visually or by using the following formula:
x =
-b
2a
By looking at theparabola and seeingthat the vertex is locatedat (2, -4), one can writethe equation for the axisof symmetry by noting thatthe x component is 2.Therefore h = 2 and theequation is "x=2". 
axis of
symmetry
vertex
(2, -4)
The x component of
the vertex is 2, therefore
the equation for the
axis of symmetry is:
Example:
x = 2
vertex
(2, 1)
axis of
symmetry
Practice:
The x component of 
the vertex is:
(
Vertex is
The equation for
the axis of
symmetry is:
x=
,
)
(
Practice:
axis of symmetry
x = 
vertex
,
)
Practice:
What is the equation
for the axis of symmetry?
x =
However, sometimes one can not determine
the axis of symmetry by looking at a graph
and identifying the "x" component of the
vertex.  In these situations, one can use the
axis of symmetry formula if the equation to 
the parabola is given.
Where "a" and "b" are taken from a quatdraticwritten in standard form; y = ax2 + bx + c
x = 
-b
2a
By just looking atthis parabola, it couldbe difficult to determinethe exact point of the vertex.  Thereforeit is more difficult towrite the formula to the"axis of symmetry".
axis of
symmetry
x = ?
vertex
( ?, ? )
So, one could use
the axis of symmetry
formula to calculate
calculate "h" (the
"x" component of the
vertex.
x = 
substitute
x =
-(-6)
2(2)
-b
2a
=
6
4
=
3
2
y = 2x2 - 6x - 1
Where
Equation to
the parabola
b = -6
a = 2
c = -1
Substititute a and b into
the formula
The equation to this 
parabola is:
y = -3x2 + 12x - 7
x = 
x = 2
a = -3
b = 12
c = -7
-(12)
2(-3)
=
12
6
x = 
axis of
symmetry
x = 2
-b
2a
Practice:
Determine the axis of
symmetry
The equation to thisparabola is:
x =
x =
y = x2 - 8x + 10
-b
2a
=
2(
-
)
b =
a =
c =
Calculate the axis of symmetry for the following:
y = -3x2 + 6x - 1
x = 
x =
x =
-b
-
2a
2(
)
Caclulate the axis of symmetry for the following:
y = 3x2 + 18x - 4
x =
x =
2(
-
)
Calculate the axis of symmetry for the following:
y = -5x2 + 30x - 12
x =
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