Name ______________________________________________ Date ________________
Algebra I
Parabolas – 11A
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)
a.
b.
c.
d.
Graph
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
_______Minimum_______
Axis of Symmetry:
[ a is the coefficient of
(1) and b is the coefficient of (
)]
___x = 2____
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.
____(2, -1)____
Finding the roots:
is why we put
The roots are where the equation
into the calculator. (The
is
)
There are usually 2 roots. To find the 1st root:
(Calc)
(intersect)
The ordered pair will be at the bottom.
To find the 2nd root:
(Calc)
crosses the
____(1, 0)_____
(intersect) DO NOT HIT ENTER!!!
. This
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.
____(3, 0)____
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
x
y
Vertex ->
-1
8
0
3
1
0
2
-1
3
0
4
3
5
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 and the axis
y
This is the best I could do.
It Shouldn’t be so flat on the
Bottom and I didn’t draw the
Arrows. Sorry!
I also couldn’t get the graph
To go through the two roots
(1, 0) and (3, 0)
x
I will give you the answers to these 4in class
.
More Examples:
1)
a.
b.
c.
d.
Graph:
Is the vertex a maximum or minimum?
Find the Axis of Symmetry.
Find the vertex.
Find the roots.
3) Graph:
2) Graph:
a. Is the vertex a maximum or minimum?
b. Find the Axis of Symmetry.
c. Find the vertex.
d. Find the roots.
4) Graph:
a.
b.
c.
d.
Is the vertex a maximum or minimum?
Find the Axis of Symmetry.
Find the vertex.
Find the roots.
a. Is the vertex a maximum or minimum?
b. Find the Axis of Symmetry.
c. Find the vertex.
d. Find the roots.