Name ______Date ______

Algebra IParabolas – 11A

Graphing the Parabola

Key Words:

  1. Vertex – The maximum or minimum point of a parabola
  2. Minimum – The lowest point on the graph of a curve
  3. Maximum – The highest point on the graph of a curve
  4. Roots – The solutions of a quadratic equation
  5. AxisofSymmetry – The vertical line containing the vertex of a parabola

1)Graph for .

  1. Is the vertex a minimum or maximum?
  2. What is the axis of symmetry?
  3. What is the vertex?
  4. 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 to find the roots of the parabola).

Min. or Max.?Look at the picture______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:The roots are where the equation crosses the . This is why we put 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.____(1, 0)_____

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.____(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
-1 / 8
0 / 3
1 / 0
2 / -1
3 / 0
4 / 3
5 / 8

Vertex ->

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) Graph: 2) Graph:

  1. Is the vertex a maximum or minimum? a. Is the vertex a maximum or minimum?
  2. Find the Axis of Symmetry. b. Find the Axis of Symmetry.
  3. Find the vertex. c. Find the vertex.
  4. Find the roots. d. Find the roots.

3) Graph: 4) Graph:

  1. Is the vertex a maximum or minimum? a. Is the vertex a maximum or minimum?
  2. Find the Axis of Symmetry. b. Find the Axis of Symmetry.
  3. Find the vertex. c. Find the vertex.
  4. Find the roots. d. Find the roots.