1. Graphing Calculator Lesson
Finding the vertex and the roots/zeros of a quadratic.
HAVE A PAPER SET UP WITH YOUR NAME AND NUMBER IT 1 THROUGH 10

2. Skill 1: Visualizing left and right
When working with functions, it is important to be able to visualize movement along the graph in terms of left-right (not up-down).
This first exercise is to help you develop this idea of left and right by tracing the cursor along the curve.
We will complete the exercise together with the document camera
Graph the equation y = x2 + 4x + 5 on your calculator before we begin.

3. Using the Trace Function
Press the TRACE button at the top and observe where the cursor is
Now press the up/down arrow keys
1.) Does the cursor move when you press the up/down arrow keys?
Now press the left and right arrow keys and observe the cursor move.
Move the cursor to the LEFT side of the vertex
2.) Write down the x-coordinate of the point (round to 2 decimal places)
Move the cursor to the RIGHT side of the vertex
3.) Write down the x-coordinate of the point (round to 2 decimal places)
CASIO
Press F1 for the TRACE option
Now press the up/down arrow keys
1.) Does the cursor move when you press the up/down arrow keys?
Now press the left and right arrow keys and observe the cursor move.
Move the cursor to the LEFT side of the vertex
2.) Write down the x-coordinate of the point (round to 2 decimal places)
Move the cursor to the RIGHT side of the vertex
3.) Write down the x-coordinate of the point (round to 2 decimal places)

4. Skill 2: Finding the vertexTI
Observe that the vertex is a minimum
Press 2nd and TRACE/CALC
Press #3 for MINIMUM
Move the cursor to the LEFT of the vertex and press ENTER
Move the cursor to the RIGHT of the vertex and press ENTER
Press ENTER through the GUESS
You should see (-2, 1) and the cursor blinking on the vertex
CASIO
Observe that the vertex is a minimum
Press F5 for G-Solve
Choose F3 for MIN
You should see (-2, 1) and the cursor on the vertex

5. Try on your own…. Graph the parabola f(x) = - x2 + 6x – 4
Observe that this time, the vertex is a maximum
We have to notice this in order to pick the correct option off the menu
4.) Find the vertex of this parabola and write your answer on your paper
NOTE: Sometimes the calculator will mix the vertex by a tiny amount. When this happens, you will see an answer like ….. when it should be -2. Just round when this happens.

6. Finding the Roots/zeros
Let’s take a few minutes to explore the left-right aspects of the roots.
Graph the equation: y = x2 -2x – 15 on your calculator and press the key to TRACE
You may not see the cursor if it is off the screen but you should see the coordinates of the vertex at the bottom. If your calculator is on a STANDARD window, those coordinates will be (0, -15).
Press the LEFT arrow key until you see the cursor appear travelling to the left (it will take about 10 to 12 presses until you can see it)
Keep moving the cursor until it is on the LEFT side of the root
5.) Write down the x-coordinate of this point
Now press the RIGHT arrow key until the cursor moves to the RIGHT side of the root
6.) Write down the x-coordinate of this point
Keep pressing the RIGHT arrow key until you see the cursor appear on the other side

7. Skill 3: Finding the roots/zerosTI
Graph y = x2 – 0.5x – 3
Observe that there are two zeros
Press 2nd and TRACE/CALC
Choose #2 for ZERO
Use the LEFT arrow key to move the cursor to LEFT of the left zero
Press ENTER
Use the RIGHT arrow key until the cursor moves to RIGHT of that zero
Press ENTER through the guess
You should see (-1.5, 0)
Press #2 for ZERO
Use the RIGHT arrow key to move the cursor to the right zero but keep it on the LEFT side
Mark the LEFT and RIGHT sides of the zero and go through the GUESS
You should see ( 2, 0)
CASIO
Graph y = x2 – 0.5x – 3
Observe the two roots
Press F5 for G-Solve
Choose F1 for ROOT
The calculator will show you one of the roots (mine showed (-1.5, 0) when I did it)
Press the left/right arrow key to move the cursor to the other root
You should see (-1.5, 0) and (2, 0) for the two roots

8. Try on Your own… Graph y = x2 – 7.5x + 12.5
Find the zeros/roots of this parabola and write your answers on your paper for #7 and #8.

9. One last problem…. Graph f(x) = -x2 + 4x + 5 9.) Find the vertex
10.) Find BOTH zeros/roots