I need help on this!!

  1, -0.5, -6.25

Step-by-step explanation:

The number in the left box is the leading coefficient. The coefficient of x^2 is 1, so that goes in the first box.

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The number in the second box is half the coefficient of x, divided by the leading coefficient:

  (1/2)(-1)/1 = -1/2

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The number in the third box (k) is the number required to make the rewritten g(x) match the original g(x). So far, we have ...

  g(x) = 1(x -1/2)^2 + k = x^2 -x -6

  x^2 -x +1/4 +k = x^2 -x -6 . . . . . expand the square

  1/4 +k = -6 . . . . . . . . . . . . . . . . . subtract the x-terms from both sides

  k = -6 1/4 . . . . . . . . . . . . . . . . . . subtract 1/4

So, you have ...

 

Part A:

The x-intercept represents the point where each side of the tunnel meets the ground. The first point is at x = 0 and the second is at x = 100 (each square is going up in 10s)

The maximum point represents the highest point of the tunnel.

The function reaches its maximum point before it decreases again in between x = 40 and x = 60

At x = 40 and x= 60, the height of the tunnel is y = 47. Translating this into the context means that at the distance of 40 units and 60 units from the point 0, the height of the tunnel is 47 units

Part B:

When x = 15, y = 25
When x = 35, y = 45

The rate of change is represented by the slope ⇒ 
(45 - 25) ÷ (35 - 15) = 20÷20 = 1 
It means that for every one unit of distance, the height increase by one unit.