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# Parabola lab day 1

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### Parabola lab day 1

1. 1. Sept 3rd Learning outcome: To discover what happens to a parabola’s graph when you change the numbers in the equation?  Launch:  1. Graph your table from last week’s pattern  2. Do you recall what this type of graph is called? x 0 1 2 3 4 n y 0 1 4 9 16 n2
2. 2. Explore: Parabola Lab 1.What happens to a parabola’s graph when you change the numbers in the equation?  a. On graph paper, graph y = (x-2)(x-2). Labeling important points including the vertex (lowest point) and line of symmetry (line that cuts the graph in half).  b. Use your graphing calculator to find the equations of 2 parabolas with different graphs that also open upward and still have a vertex at (2, 0). Use 2 different colored pencils to add the sketches along with the equations to the graph from #1.
3. 3. Explore: Parabola Lab  c. Use your calculator to find the equation of 2 different parabolas that open downward, each with its vertex on the x-axis at x = 2. Use 2 different colored pencils to add the sketches along with the equations to the graph from #1 a and b.  d. Use your calcuator to find the equation of a parabola that opens downward with a vertex of (-4, 0). What is the equation of your parabola’s line of symmetry?  e. Choose a new point on the x-axis and find at least 3 equations of parabolas that touch the x- axis only at that one point.
4. 4. Explore: Parabola Lab part 2  2. Use your graph y = x2 from the launch to do the following:  a. Find a way to stretch y = x2 vertically (make it narrower), but the vertex stays in the same place. Use a colored pencils to add the sketch along with the equations to the graph from the launch.  b. Find a way to compress y = x2 vertically (make it flatter), but the vertex stays in the same place. Use a colored pencils to add the sketch along with the equations to the graph from the launch.  c. Find a way to open y = x2 downward, but the vertex stays in the same place and is the same shape as y = x2. Use a colored pencils to add the sketch along with the equations to the graph from 2a.
5. 5. Explore: Parabola Lab part 2  2d. Find a way to move y = x2 5 units down (but remain the same shape and size and vertex at (0,5)). Use a colored pencils to add the sketch along with the equations to the graph from the launch.  2e. Find a way to move y = x2 3 units to the right (but remain the same shape and size and vertex at (3,0)). Use a colored pencils to add the sketch along with the equations to the graph from the launch.  2f. Find a way to move y = x2 3 units left and stretch vertically Use a colored pencils to add the sketch along with the equations to the graph from the launch.
6. 6. Parabola Lab challenge  3. Find a way to change the equation y = x 2 parabola vertically compressed, open down, move six units up and move two unites to the left. Where is the vertex of your new parabola?
7. 7. Summary  Now that you are a parabola expert can you write a general equation for a parabola that can be stretched or shifted any direction?