What are the zeros of y = x^3 - 3x graphically?

The zeros of \( y = x^3 - 3x \) are \( x = -\sqrt{3} \), \( x = 0 \), and \( x = \sqrt{3} \).

To find the zeros of the function \( y = x^3 - 3x \) graphically, we need to identify the points where the graph intersects the x-axis. These points are where the value of \( y \) is zero. In other words, we solve the equation \( x^3 - 3x = 0 \).

First, we can factorise the equation:
\[ x^3 - 3x = x(x^2 - 3) = 0 \]

This gives us two factors: \( x = 0 \) and \( x^2 - 3 = 0 \). Solving \( x^2 - 3 = 0 \) involves taking the square root of both sides:
\[ x^2 = 3 \]
\[ x = \pm\sqrt{3} \]

So, the solutions are \( x = -\sqrt{3} \), \( x = 0 \), and \( x = \sqrt{3} \). These are the points where the graph of \( y = x^3 - 3x \) crosses the x-axis.

When you plot the graph of \( y = x^3 - 3x \), you will see it intersects the x-axis at these three points. The graph has a characteristic cubic shape, with a local maximum and minimum, and it crosses the x-axis at \( x = -\sqrt{3} \), \( x = 0 \), and \( x = \sqrt{3} \). This visual representation helps to confirm the zeros we calculated algebraically.