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Find the equation of the line of symmetry and the coordinates of the turning point of the graph of \(y = x^2 - 6x + 4\)

Writing \(y = x^2 - 6x + 4 \) in completed square form gives \(y = (x - 3)^2 - 5\).

Squaring positive or negative numbers always gives a positive value. The lowest value given by a squared term is 0, which means that the minimum value of the term \((x - 3)^2 - 5\) is given when \(x = 3\). This also gives the equation of the line of symmetry for the quadratic graph.

The value of \(y\) when \(x = 3\) is -5. This value is always the same as the constant term in the completed square form of the equation.

So the graph of \(y = x^2 - 6x + 4\) has a line of symmetry with equation \(x = 3\) and a turning point at (3, -5).