Properties of a quadratic function

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.

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