Name ______________________________________________ Date ________________ Color _____________
Algebra I
Ms. Hahl
Graphing the Parabola
Key Words:
a. Vertex – The maximum or minimum point of a parabola
b. Minimum – The lowest point on the graph of a curve
c. Maximum – The highest point on the graph of a curve
d. Roots – The solutions of a quadratic equation
e. Axis of Symmetry – The vertical line containing the vertex of a parabola
1) Graph
a.
b.
c.
d.
for
.
Is the vertex a minimum or maximum?
What is the axis of symmetry?
What is the vertex?
What are the roots?
The first thing you should do is put the equation into the calculator. Put
into
While you are in the
screen, you might as well put in
into (you will need to use
find the roots of the parabola).
Min. or Max.?
Look at the picture
.
to
___________________
Axis of Symmetry:
[ a is the coefficient of
(1) and b is the coefficient of (
)]
_______
Finding the vertex:
If the axis of symmetry is an integer, then you can find the ordered pair for the vertex in
the table. If not, we will use the calculator.
(Calc)
(Value)
(
)
The ordered pair for the vertex will appear on the bottom of the screen.
____________
Finding the roots:
The roots are where the equation
We put
into the calculator. (The
is
st
There are usually 2 roots. To find the 1 root:
(Calc)
(intersect)
The ordered pair will be at the bottom.
crosses the
)
. This is why
___________
To find the 2nd root:
(Calc)
(intersect) DO NOT HIT ENTER!!!
You must move the cursor using the blue left and right arrows (not up and down) close
to the 2nd root. Once you are close then press:
The ordered pair will be at the bottom.
__________
Creating the Table:
To create the table you will take your vertex for a starting point. From that point you
will choose 3 numbers less than your
and 3 numbers greater than your
.
-1
0
1
2
3
4
5
8
3
0
-1
0
3
8
Graphing the Parabola: Once all of the previous parts are filled in you have all of the needed information to
graph the parabola. 1st – Plot the points from your table. 2nd – Draw a smooth curve to connect
your points. 3rd – Label your graph.
More Examples:
1) Graph:
a. Is the vertex a maximum or minimum?
b. Find the Axis of Symmetry.
c. Find the vertex.
d. Find the roots.
2) Graph:
a. Is the vertex a maximum or minimum?
b. Find the Axis of Symmetry.
c. Find the vertex.
d. Find the roots.
3) Graph:
e.
f.
g.
h.
Is the vertex a maximum or minimum?
Find the Axis of Symmetry.
Find the vertex.
Find the roots.
4) Graph:
a. Is the vertex a maximum or minimum?
b. Find the Axis of Symmetry.
c. Find the vertex.
d. Find the roots.