The height 'h' (in feet) of a ball in a baseball game can be modeled by h = -16t² + 28t + 8 , where 't' is the time (in seconds).
a. do both t-intercepts of the graph of the function have meaning in this situation? explain.
b. no one caught the ball. after how many seconds did the ball hit the ground?

  a)  No. t < 0 is not part of the useful domain of the function

  b) 2.0 seconds

Step-by-step explanation:

a) A graph of the function is shown below. It shows t-intercepts at t=-0.25 and t=2.0. We presume that t is measured forward from some event such as the ball being thrown or hit. The model's predicted ball location has no meaning prior to that event, when values of t are negative.

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b) It is convenient to use a graphing calculator to find the t-intercepts. Or, the equation can be solved for h=0 any of several ways algebraically. One is by factoring.

  h = 0 = -16t² +28t +8 . . . . . . . . . . . . the ball hits the ground when h = 0

  0 = -4(4t² -7t -2) = -4(4t +1)(t -2)

This has t-intercepts where the factors are zero, at t=-1/4 and t=2.

The ball will hit the ground after 2 seconds.

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.