Question

HELP PLEASE!!!!!!!!!!!!! S=-16t^2+64t+25
After how many seconds will the rock reach its maximum height?

Answer 1

should that be 64t?

Answer 2

yes sorry

Answer 3

the figure is a parabola. The negative tells you it is like an upside down u. therefore it has a maximum value. That value is at the vertex of the parabola.
To find the vertex: (1) Let x = -b/2a (2) take the number you must found and replace x with it in the original equation to solve for y.

Answer 4

do you know how to find -b/2a?

Answer 5

b would be 64?

Answer 6

and a would be -16

Answer 7

yes

Answer 8

Can't you also use derivatives to find the vertex?

Answer 9

Lol ... I didn't realize you were at that level

Answer 10

so it would be 2

Answer 11

yes ... using derivatives, you get -32t+64 and the zero of that is where it changes "direction" (increasing/decreasing). You still get 2 and you plug that value into the original equation to get the value for S which is the actual max

Answer 12

\[-16(2)^{2}+64(2)+25\]

Answer 13

with the answer being 89 feet