# Identify the domain of the equation y = x^{2} - 6x + 1.

x ≤ 3, x ≥ - 8, x ≥ - 2, All real numbers

The domain of a function is all real numbers except where the function is undefined. The domain is (∞, -∞).

We can write the equation in the vertex form of a parabola as a(x - h)^{2} + k. The vertex of parabola is (h, k).

By using the method of completing the square we get,

y = x^{2} - 6x + 1

= (x - 3)^{2} + (-8)

Since the value of a is positive, the graph of the parabola will open upwards.

The vertex of parabola is (3, -8).

Hence, the domain of the graph y = x^{2} - 6x + 1 is all real numbers

The domain of the parabola is (3, -8) and range (-8, ∞).

## Identify the domain of the equation y = x^{2} - 6x + 1.

**Summary:**

The domain of the graph y = x^{2} - 6x + 1 is (-∞, ∞) (all real numbers) and the range is (-8, ∞).