The graph below shows the height of a tunnel f(x), in feet, depending on the distance from one side of the tunnel x, in feet:

graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 120, 0. the vertex is at 60, 35.

part a: what do the x-intercepts and maximum value of the graph represent? what are the intervals where the function is increasing and decreasing, and what do they represent about the distance and height?

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?

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.

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.