1. Use the slider to change the value of h. Explain in complete sentences how the graph changes as h changes. Consider positive values, negative values, and h = 0.
2. Use the slider to change the value of k. Explain in complete sentences how the graph changes as k changes. Consider positive values, negative values and k = 0.
3. Use the slider to change the value of a. Explain in complete sentences how the graph changes as a changes. Consider positive and negative values.
4. What happens to the graph when a = 0? Explain why you think this happens.
5. Now look at the vertex which is labeled A. Move each of the sliders until you can determine which parts of the equation are related to the vertex. Explain the relationship between the equation in the form y = a(x - h)² + k and the coordinates of the vertex of the parabola.
6. Make a conjecture as to the coordinates of the vertex of the parabola with the equation y = 2(x - 3)² + 4. Write down your conjecture.
7. Now enter the equation y = 2(x - 3)² + 4 in the input bar at the top of the page to check your answer. If your conjecture was wrong, explain why.
8. Make a conjecture as to the coordinates of the vertex of the parabola with the equation y = 1/3 (x + 2)² - 5.
9. Check your answer. If your conjecture was wrong, explain why.