Look at the parametrically defined function below and compare it to the previous one. Also examine the Table below.
18
Expression 19: left parenthesis, "b" "t" plus 2 , 576 minus 16 left parenthesis, "b" "t" , right parenthesis squared , right parenthesisbt+2,576−16bt2
domain t Minimum: 00
less than or equal to "t" less than or equal to≤t≤
domain t Maximum: 11
19
"x"x
"y" equals 576 minus 16 left parenthesis, "x" minus 2 , right parenthesis squaredy=576−16x−22
22
r1c2:
r1c3:
33
r2c2:
r2c3:
44
r3c2:
r3c3:
55
r4c2:
r4c3:
66
r5c2:
r5c3:
r6c2:
r6c3:
20
NOW FOR THE STUDENT INVESTIGATION AND QUESTIONS...
21
1. Describe the relationship between the 2 graphs. Be specific.
22
2. Explain the effect of the "+2" in "bt+2" graphically. Why is the domain for the 2nd function 2 <=x<=6?
23
3. Explain algebraically how "576-16(bt)^2" was transformed to 576-16(x-2)^2.
24
4. Fill in the missing coordinates for each graph: Green (___,512); Orange (___,512)
25
5. 'a' and 'b' were both set to 4. What value do we need for 'a' and 'b' in order for the graphs to terminate on the x-axis? Try it! Adjust as needed.
26
7. PLAY the slider for 'a' by pressing the PLAY button to the left. Describe what happens. Now do the same for 'b'. Explain why the curves are repeatedly being traced and 'erased'.
