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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
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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.
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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)
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Skill 2: Finding the vertex
TI 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
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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.
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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
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Skill 3: Finding the roots/zeros
TI 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
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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.
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One last problem…. Graph f(x) = -x2 + 4x + 5 9.) Find the vertex
10.) Find BOTH zeros/roots
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