---
title: "The electric potential \\(V\\) in a region of space along the \\(x\\)-axis is given by the function \\(V(x) = \\alpha x^2\\), where \\(\\alpha\\) is a positive constant. The graph shows \\(V\\) as a function of position \\(x\\) over the interval \\(-x_0 \\le x \\le x_0\\). Which of the following graphs best represents the \\(x\\)-component of the electric field, \\(E_x\\), as a function of position \\(x\\) over the same interval?"
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url: "https://nerd-notes.com/ubq/124602/"
date_modified: "2026-09-28T14:08:47+00:00"
---

# The electric potential \(V\) in a region of space along the \(x\)-axis is given by the function \(V(x) = \alpha x^2\), where \(\alpha\) is a positive constant. The graph shows \(V\) as a function of position \(x\) over the interval \(-x_0 \le x \le x_0\). Which of the following graphs best represents the \(x\)-component of the electric field, \(E_x\), as a function of position \(x\) over the same interval?

The electric potential \(V\) in a region of space along the \(x\)-axis is given by the function \(V(x) = \alpha x^2\), where \(\alpha\) is a positive constant. The graph shows \(V\) as a function of position \(x\) over the interval \(-x_0 \le x \le x_0\). Which of the following graphs best represents the \(x\)-component of the electric field, \(E_x\), as a function of position \(x\) over the same interval?

![A Cartesian coordinate plane with horizontal axis labeled x and vertical axis labeled V. The horizontal axis extends symmetrically from -x_0 to +x_0, with tick marks labeled -x_0 at the far left, 0 at the origin, and +x_0 at the far right. The vertical axis extends upward from 0, with a single tick mark at the maximum height labeled V_0. A smooth solid curve forms a symmetric parabola opening upward with its vertex located at the origin (0, 0). The curve passes through the points (-x_0, V_0) and (+x_0, V_0). Horizontal and vertical dashed line segments connect (-x_0, V_0) to the axes and (+x_0, V_0) to the axes. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604526-aEX4y1.jpg)

- **A.** Graph A
- **B.** Graph B
- **C.** Graph C
- **D.** Graph D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124602/*