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# Parabola lab day 2

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### Parabola lab day 2

1. 1. Sept 4th Learning outcome: To discover what happens to a parabola’s graph when you change the numbers in the equation?  Launch:  1. How would you change the equation y = x2 to have the graph open down?  2. How would you change the equation y = x2 to have the graph move 6 units up?  How would you change the equation y = x2 to have the graph move 3 units right?
2. 2. Explore: Graphing tool Let’s try it: http://www.cpm.org/flash/technology/tran sform_parabolas.swf Answer the following for y = a(x-h)2 + k 1. Which parameter (a, h or k) effects: a. Orientation (up or down facing) b. Shift up or down? c. Shift left or right?
3. 3. Explore: Predict  1. For each equation, predict the vertex, orientation (up or down), and whether it will be a vertical stretch (narrower) or compression (wider) of y = x2  a. y = (x + 9) 2 b. y = x2  c. y = 3x2 d. y = 1/3 (x-1)2  e. y = -(x-7)2 +6 f. y = 2(x+3)2 - 8  g. Check your predictions with a calculator and describe how you need to change your predictions
4. 4. Explore: Graphing without a calculator  2. Graph each equation without making a table or using a calculator. What are your strategies?  a. y = (x-7)2 – 2 b. y = 0.5 (x+3)2 + 1
5. 5. Summary  3. Now we are going to look at quadratics in standard form y = ax2 +bx + c  a. What is the orientation of y = 2x2 +4x - 30? (up or down facing)  b. What is the stretch factor of y = 2x2 +4x - 30? C. Can you look at =y = 2x2 +4x -30 and figure out the vertex? (reminder of how: vertex = -b/2a)