If a projectile is fired straight upward from the ground with an initial speed of 96 feet per second, then its height h in feet after t seconds is given by the function h(t)= -16t^2 + 96t. Find the maximum height of the projectile.

144 feet

Step-by-step explanation:

The quadratic equation is:

The general form of a quadratic is  

So, we can match the equations and say:

a = -16

b = 96

c = 0

Now, for quadratic equations, the max value occurs at and the max value is what we get when we put that number in the function. First, lets find the value on which is occurs:

Now, put x = 3 into the equation:

The max height of projectile is 144 feet

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

i don't even know man. edge inuity be messing with us. i had to ask a question too.