Question

In Gabriel's village there is an electrical wire suspended between two poles across a gully.the poles are on the edge of the gully and the wire is at the same height on both sides of the gully. The curve of the wire can be modeled by the equation h = (d - 6)² + 3
Where h is the height, in meters, of the wire above the floor of the gully and d is the distance, in meters, from the left-hand post.
Use this information to answer the following questions:
A. Draw the graph of h = (d - 6)² + 3 for the values of distance, d, from 0 to 12.
B. What is the minimum height that the wire is above the floor of the gully?
C. a) how far apart are the two poles?
b) how is this shown on the graph?

Answer 1

To draw the graph of the equation h = (d - 6)² + 3, we can create a coordinate system where the horizontal axis represents the distance (d) and the vertical axis represents the height (h).

A. Plotting the graph for d values from 0 to 12:

- For d = 0, we can substitute it into the equation:
h = (0 - 6)² + 3
h = 36 + 3
h = 39
So the first point on the graph is (0, 39).

- For d = 1:
h = (1 - 6)² + 3
h = 25 + 3
h = 28
The second point on the graph is (1, 28).

- Continue in the same way for d = 2, 3, 4, ..., 12 to get the remaining points.

Plot the points and connect them with a smooth curve. The resulting graph should look like a parabola opening upwards.

B. The minimum height that the wire is above the floor of the gully can be found by identifying the vertex of the parabola. In this case, the vertex occurs when d = 6 because of the equation's form (d - 6)².

When d = 6, h = (6 - 6)² + 3 = 3.
So the minimum height that the wire is above the floor of the gully is 3 meters.

C. a) The distance between the two poles can be calculated by finding the x-coordinate values of the points where the parabola intersects the x-axis. In this case, the parabola does not intersect the x-axis, so there is no "zero" value for d. Therefore, the distance between the two poles is undefined.

C. b) On the graph, the distance between the two poles is shown by the x-axis range covered by the parabola, which in this case is from d = 0 to d = 12.