Session 2:Exploring Quadratic Curves - Questions

Exploring y=ax^2

1. Make a table of values for y=x^2, using positive, negative, and zero values of x. What do you notice? Is the graph symmetric? If so, about which axis? What is the shape of the graph? What is the lowest/highest point?

2. Plot y=2x^2 and y=0.5x^2 on the same graph. What do you notice about the shape of the graphs? Which one is wider? Which one is narrower? What is the lowest/highest point of each graph?

3. Plot y=-x^2 and y=-2x^2 on the same graph. What do you notice about the shape of the graphs? What is the lowest/highest point of each graph?

4. Based on your observations, what is the effect of the coefficient of x^2 on the shape of the graph? What is the effect of a negative coefficient?

Exploring y=ax^2+c

5. What happens when you plot y=x^2+2 and y=x^2-3? What do you notice about the shape of the graphs? What is the lowest/highest point of each graph? Do these graphs intersect the y-axis? If so, where? How does the graph of y=x^2 change when 2 is added or 3 is subtracted? Which way does it shift?

6. Plot the graphs of y=2x^2, y=2x^2+4, y=2x^2-4, y=-2x^2+4, y=-2x^2-4. What do you notice about the shape of the graphs? What is the lowest/highest point of each graph? Do these graphs intersect the x-axis and y-axis? If so, where?

7. Based on your observations, what is the effect of the coefficient of x^2 on the shape of the graph? What is the effect of a negative coefficient? What is the effect of the constant term c on the shape of the graph?

Exploring y=ax^2+bx

8. Plot the graphs of y=x^2+2x and y=x^2-2x, What happens to the graph of y=x^2 when 2x is added or subtracted? Does the shape of the graph change? Does the lowest/highest point change? Does the point of intersection of the axis change?

9. Based on your observations, what is the effect of the coefficient of x on the shape of the graph? What is the effect of a negative coefficient?

Exploring y=ax^2+bx+c

10. Plot the graphs of y=x^2+2x+2, y=x^2+2x-2. What happens to the graph of y=x^2+2x when 2 is added or subtracted? Does the shape of the graph change? Does the lowest/highest point change? Does the point of intersection of the axis change?

Summarising the observations

11. Based on your observations, what is the effect of the coefficient of x^2 on the shape of the graph? What is the effect of a negative coefficient? What is the effect of the coefficient of x on the shape of the graph? What is the effect of a negative coefficient? What is the effect of the constant term c on the shape of the graph?