Investigate the properties of a quadratic function of the form [math]f(x)=a(x-p)^2+q[/math]
NB: Start with [math]a=0[/math],[math]p=0[/math] and[math]q=0[/math] 1: Why is the function initially a straight line? 2: Leave [math]a=0[/math] and adjust the value of [math]q[/math]. What happens to the function? 3: Leave [math]a=0[/math] and adjust the value of [math]p[/math]. Does anything appear to happen to the function? 4: Adjust the value of [math]a[/math] to be positive. How did the function change? Why is it not a straight line? 5: Adjust the value of [math]a[/math] to be negative. How did the function change compared to 4? 6: Describe the effect that [math]a[/math] has on the function. 7: Ensure that [math]a[/math] is NOT equal to [math]0[/math]. 8: Adjust the value of [math]q[/math]. How does the function change? 9: Adjust the value of [math]p[/math]. How does the function change? Give two differences in the way the function changes compared to when you adjusted [math]q[/math]. 10: Identify the turning point of the function. Adjust the values of [math]p[/math] and [math]q[/math]. How do they relate to the turning point? 11: Describe the effect that [math]p[/math] has on a quadratic function. 12: Describe the effect that [math]q[/math] has on a quadratic function. 13: Now set [math]a=0[/math]. Does the function change as you adjust [math]p[/math]. Give a reason for your answer.