Investigate the properties of a quadratic function of the form [math]f(x)=a(x-h)^2+k[/math].

NB: [b]Start with [/b][math]a=0[/math][b],[/b][math]h=0[/math][b] and[/b][math]k=0[/math][br][br]1: Do you see a horizontal line? (If not, see above.) Why is the function initially a straight line? [i]Hint: Look at the equation.[/i][br]2: Leave [math]a=0[/math] and adjust the value of [math]k[/math]. What happens to the function? [i]Reset.[/i][br]3: Leave [math]a=0[/math] and adjust the value of [math]h[/math]. Does anything appear to happen to the function? [i]Reset.[/i][br]4: Adjust the value of [math]a[/math] to be positive. How did the function change? Why is it not a straight line?[br]5: Adjust the value of [math]a[/math] to be negative. How did the function change compared to question 4?[br]6: Describe the effect that [math]a[/math] has on the function.[br]7: Ensure that [math]a[/math] is NOT equal to [math]0[/math].[br]8: Adjust the value of [math]k[/math]. How does the function change? [br]9: Adjust the value of [math]h[/math]. How does the function change? Give two differences in the way the function changes compared to when you adjusted [math]k[/math]. [i]Reset, and ensure a is NOT equal to 0.[/i][br]10: Identify the turning point of the function. Adjust the values of [math]h[/math] and [math]k[/math]. How do they relate to the turning point?[br]11: Describe the effect that [math]h[/math] has on a quadratic function.[br]12: Describe the effect that [math]k[/math] has on a quadratic function.[br]13: Now set [math]a=0[/math]. Does the function change as you adjust [math]h[/math]. Give a reason for your answer.