The coordinates of the turning point and the equation of the line of symmetry can be found by writing the quadratic expression in completed square form.

Find the equation of the line of symmetry and the coordinates of the turning point of the graph of

The coefficient of is positive, so the graph will be a positive U-shaped curve.

Writing in completed square form gives

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 is given when

is also the equation of the line of symmetry

When , so the turning point has coordinates (3, -5)

- Question
Sketch the graph of , labelling the points of intersection and the turning point.

The coefficient of is positive, so the graph will be a positive U-shaped curve.

Factorising gives and so the graph will cross the -axis at and .

The constant term in the equation is -3, so the graph will cross the -axis at (0, -3)

Writing in completed square form gives , so the coordinates of the turning point are (1, -4).