Question

the graph is a two - dimensional representation of the curve a manufacturer uses to define the shape of a commercial satellite in feet. a machine is programmed to make a horizontal cut along the x - axis, trimming the sides of the satellite dish. what is the resulting width of the satellite dish, in feet? 4 ft, 6 ft, 8 ft, 12 ft. the graph has points (-6, 0), (6, 0) and (0, -4).

Explanation:

Step1: Identify x-intercepts

The x-intercepts of the parabola (where the graph intersects the x-axis) are at \((-6, 0)\) and \((6, 0)\).

Step2: Calculate the width

The width of the satellite dish is the distance between these two x-intercepts. The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) on the x-axis (where \(y_1 = y_2 = 0\)) is given by \(|x_2 - x_1|\). Here, \(x_1=-6\) and \(x_2 = 6\), so the distance is \(|6 - (-6)|=|12| = 12\) feet? Wait, no, wait. Wait, the horizontal cut is along the x - axis, so the two points where the graph meets the x - axis are \((-6,0)\) and \((6,0)\). The width is the distance between these two points. The formula for the distance between two points \((x_1,0)\) and \((x_2,0)\) is \(x_2 - x_1\) (since \(y\) - coordinates are the same). So \(6-(-6)=12\)? But wait, let's check the graph again. Wait, the points are \((-6,0)\) and \((6,0)\). The distance between them is \(6 - (-6)=12\)? But wait, the options include 12 ft. Wait, but let's confirm. The x - intercepts are at \(x=-6\) and \(x = 6\). The width is the difference between these two x - values (since it's horizontal, along the x - axis). So \(6-(-6)=12\) feet.

Wait, but let me re - check. The problem says "a horizontal cut along the x - axis, trimming the sides of the satellite dish". The satellite dish's shape is the parabola, and the cut is along the x - axis, so the width is the distance between the two x - intercepts. The x - intercepts are at \((-6,0)\) and \((6,0)\). The distance between \(-6\) and \(6\) on the x - axis is \(6-(-6)=12\) feet. So the resulting width is 12 feet.

Answer:

D. 12 ft