What are the x-intercept and y-intercept of the graph of the equation y = x² + 6?

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To find the x-intercept and y-intercept of the equation y = x² + 6, we need to evaluate the function at specific points.

X-Intercept:

The x-intercept occurs when y = 0. To find it, we set the equation equal to zero:

0 = x² + 6

Rearranging gives us:

x² = -6

Since the square of a real number cannot be negative, there are no real solutions to this equation. Therefore, there are no x-intercepts for the graph of this function.

Y-Intercept:

The y-intercept occurs when x = 0. To find it, we substitute x = 0 into the equation:

y = (0)² + 6

Calculating this gives:

y = 6

Thus, the y-intercept is located at the point (0, 6).

Summary:

In summary, the graph of the equation y = x² + 6 has:

  • No x-intercepts
  • Y-intercept at (0, 6)

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