Question

a catapult launches a boulder with an upward velocity of 122 ft/s. the height of the boulder, (h), in feet after t seconds is given by the function h(t)--16t^2+122t+10. how long does it take the boulder to reach its maximum height? whats the boulder's maximum height? round to the nearest hundredth, if necessary.

Answer 1

reaches a maximum height of 15.42 feet after 7.71 seconds
reaches a maximum height of 7.71 after 3.81 seconds
reaches a maximum height of 242.56 feet after 7.62 seconds
reaches a maximum height of 242.56 feet after 3.81 seconds

Answer 2

one way would be to convert the formula to vertex form by completing the square

Answer 3

-16t^2+122t+10

=-16( t^2 - 7.625t) + 10

= -16[ {t - 3.8125)^2 - 3.8125^2)] + 10

= -16(t - 3.8125) ^2 + 232.5625 + 10

= -16(t - 3.81)^2 + 242.56

Answer 4

- so the time is 3.81 and maximum height is 242.56

Answer 5

vertex form of a quadratic is

a(x - b^2 + c

where the vertex is at (b , c)

Answer 6

oh man thank you so mcuh i was struggling so hard with that one