Plz help me!! Part A: What do the x-intercepts and maximum value of the graph represent? Part B: What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit?

Part C: What is an approximate average rate of change of the graph from x= 1 to x = 3, and what does this rate represent?​

x - intercepts (0, 0) and (120, 0)

Vertex is at (60, 35).

Part A: What do the x-intercepts and maximum value of the graph represent?

The x-intercepts represent the points at the ground, so with that you have the width of the tunnel at ground level is 120 ft - 0 ft = 120 ft..

The vertex represents the maximum height, which is at the center of the tunnel. So, you know that the maximum height is at x = 60 ft and it is 35 ft

What are the intervals where the function is increasing and decreasing, and what do they represent about the distance and height?

The increasing interval is (0,60), and the decreasing interval is (60,120).

That represents that the height increase from the left border (x = 0) until the center of the tunnel (x = 60 ft), reaching a height of 35 ft, and starts to decrease toward the right border until the ground level (x = 120).

Part B: What is an approximate average rate of change of the graph from x = 20 to x = 35, and what does this rate represent?

Find the y -coordinate for x = 20 and for x = 35. Supposse they are (I do not have the figure, because you did not include it) y = 15 and y = 45.

Then the average rate of change is equal to [change in height] / [change in x] = [45 - 15] / [35 - 20] = 30 / 15 = 2.

Remember that you have to use the real approximate values for the height that you can read in the figure. If the number is positive means that the height is increasing in that interval.

Here's link to the

cutt.ly/nz6VGda

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.