## anonymous one year ago The function h= is used to model fireworks being launched (or projected) into the air. The function models the height h after x seconds. a) How long will it take the fireworks to reach their greatest height? b) How high will the fireworks be their greatest height?

1. anonymous

$h=-16x ^{2}+160x+4$

2. xapproachesinfinity

to find the max height you need to take derivative

3. TrojanPoem

Find maxima using derivative as xapproaches said then you will get the time put it in the main function and you will get the height.

4. xapproachesinfinity

$$\frac{dh}{dx}=-32x+160$$ set this equal 0 to find the time it takes to reach maximum

5. anonymous

hello mam, i would like to know whether u are used to taking derivatives..?

6. xapproachesinfinity

you can actually discard calculus and do it with basic tools

7. xapproachesinfinity

that's just a parabola! and you learned that the prabolas has max at $$\left (\frac{-b}{2a}, h(\frac{-b}{2a})\right )$$

8. xapproachesinfinity

when a<0 that is

9. xapproachesinfinity