2) Scott kicks a soccer ball during a game. The height of the ball, in feet, can be modeled by the function f(x) = -16x2 + 48x, where x is the time in seconds after he kicks the ball.
When does this occur?
What is the maximum height achieved by the ball?
ow long is the ball in the air?
How high is the ball after 1 second?
What is a reasonable domain for this situation?
What is a reasonable range?
Oop

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!

0/5 is 0, 2/0 is undefined, and 0/0 is indeterminate.

step-by-step explanation:

hope my answer has you!