# Properties of a quadratic function

- Author:
- Matthew Gill

Investigate the properties of a quadratic function of the form

NB: Start with , and
1: Why is the function initially a straight line?
2: Leave and adjust the value of . What happens to the function?
3: Leave and adjust the value of . Does anything appear to happen to the function?
4: Adjust the value of to be positive. How did the function change? Why is it not a straight line?
5: Adjust the value of to be negative. How did the function change compared to 4?
6: Describe the effect that has on the function.
7: Ensure that is NOT equal to .
8: Adjust the value of . How does the function change?
9: Adjust the value of . How does the function change? Give two differences in the way the function changes compared to when you adjusted .
10: Identify the turning point of the function. Adjust the values of and . How do they relate to the turning point?
11: Describe the effect that has on a quadratic function.
12: Describe the effect that has on a quadratic function.
13: Now set . Does the function change as you adjust . Give a reason for your answer.