Quadratic functions in Vertex Form

Investigate the properties of a quadratic function of the form

Exploration: Record your answers on a separate sheet of paper or document.

NB: Start with

and

1: Do you see a horizontal line? (If not, see above.) Why is the function initially a straight line? Hint: Look at the equation. 2: Leave

and adjust the value of

. What happens to the function? Reset. 3: Leave

and adjust the value of

. Does anything appear to happen to the function? Reset. 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 question 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

. Reset, and ensure a is NOT equal to 0. 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.