Answer:
a. 272 feet
b. 8 seconds
c. 1,296 feet
d. 17 seconds
Step-by-step explanation:
A) The function is [tex]-16t^{2}[/tex]+256t+272
The y-intercept is 272, meaning that's where he started at (since he launched himself when x=0).
B) You can find this either by entering it into a calculator and looking at the table, or by factoring (no calculator). To factor, separate -16 from the rest of the terms since everything in the polynomial ([tex]-16t^{2}[/tex]+256t+272) can be divided by -16. It should look like this:
-16([tex]t^{2}[/tex]-16t-17)
Then factor it:
-16(t-17)(t+1)
From the factored version, we can tell that the x-intercepts are 17 and -1. The maximum would be right in the middle of these. 8 is the value directly in between 17 and -1.
C) To find the y-value of the maximum, just solve the original equation using 8, the x-value for the maximum:
-16([tex]8^{2}[/tex])+256(8)+272
-16(64)+2,048+272
-1,024+2,320=1,296
D) We already figured out the x-intercepts earlier. Since he can't reach the ground at -1, we know that he landed (touched the ground at y=0) at x=17.
