Question 1171303
Absolutely! Let's break down how to find the equation for the parabolic cross-section of the satellite dish.

**1. Set up a Coordinate System**

To make this problem easier, let's set up a coordinate system:

* Place the vertex of the parabola at the origin (0, 0).
* Let the axis of symmetry of the parabola be the y-axis.
* Since the receiver is above the vertex, the parabola opens upwards.

**2. Understand the Given Information**

* The vertex is 4 feet away from the surface of the station, and the receiver is 7 feet above the vertex.
* This means the receiver is located at the point (0, 7).
* The standard equation of a parabola that opens upwards with its vertex at the origin is:
    * x² = 4py
    * Where 'p' is the distance from the vertex to the focus (the location of the receiver).

**3. Find the Value of 'p'**

* In this case, the distance from the vertex (0, 0) to the receiver (focus) (0, 7) is 7 feet.
* Therefore, p = 7.

**4. Write the Equation**

* Substitute p = 7 into the standard equation:
    * x² = 4(7)y
    * x² = 28y

**Therefore, the equation that best models the parabolic cross-section of the satellite dish is x² = 28y.**

**Visual Explanation**

Imagine the satellite dish in a 2D plane:

* The vertex is at (0, 0).
* The receiver (focus) is at (0, 7).
* The parabola opens upwards along the y-axis.

The equation x² = 28y represents this parabolic shape.