Problema Solution
You and a friend are hiking in the mountains. You want to climb too a ledge that is 20 ft. above you. The height of the grappling hook you throw is given by the function h(t)= -16t^2 - 32t +5 . What is the maximum height of the grappling hook? Can you throw it high enough to reach the ledge?
Answer provided by our tutors
the given parabolic function is
h(t)= -16t^2 - 32t +5
since the quotient in front of t^2 is -16<0 follows the function has maximum
the maximum of a parabolic function f(x) = ax^2 + bx + c is given by the formula
fmax = c - b^2/(4a)
in our case we have
h max = 5 - (32)^2/(4*(-16))
h max = 21 ft
the maximum height is 21 ft
we can also see that if we draw the function
click here to see the graph of the function
20 < 21 follows you can try the high enough.