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

The coefficient of \(x^2\) is positive, so the graph will be a positive U-shaped curve.

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 turning point of the graph \(y = x^2 –6x + 4\) is given when \(x = 3\)

\(x = 3\) is also the equation of the line of symmetry

When \(x = 3\), \(y = -5\) so the turning point has coordinates (3, -5)