A catapult launches a boulder with an upward velocity of 148 ft/s. The height of the boulder (h) in feet after t seconds is given by the function h = –16t² + 148t + 30. How long does it take the boulder to reach its maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary. (I don't understand these questions at all :/)
9.25 s; 30 ft
4.63 s; 640.5 ft
4.63 s; 1,056.75 ft
4.63 s; 372.25 ft

Question

A catapult launches a boulder with an upward velocity of 148 ft/s. The height of the boulder (h) in feet after t seconds is given by the function h = –16t² + 148t + 30. How long does it take the boulder to reach its maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary.  (I don't understand these questions at all :/)
9.25 s; 30 ft
4.63 s; 640.5 ft
4.63 s; 1,056.75 ft
4.63 s; 372.25 ft

across · Answer

$$f(t)=-16t^2+148t+30$$Do you know how to differentiate?

anonymous · Answer

nope :/

across · Answer

But you are taking calculus, right?

anonymous · Answer

no. algebra one

across · Answer

And here sat I thinking that this was a calculus course. I must have had you confused all along.

across · Answer

It is a pain in the butt to solve this using algebra alone: You have to find the roots of that polynomial to find the vertex.

across · Answer

And to do that, you may have to either factor or make use of the good-old$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

across · Answer

Then$$\frac{x_2+x_1}{2}$$will be your vertex.

anonymous · Answer

ohh. thank ya