Worked examples
The graph below has a turning point (3, -2). Write down the nature of the turning point and the equation of the axis of symmetry.
Answer
The parabola shown has a minimum turning point at (3, -2). The equation of the axis of symmetry is \(x = 3\).
Question
For the parabola \(y=(x+6)(x-4)\) determine the coordinates and nature of its turning pont and the equation of the axis of symmetry.
The roots are \(x=-6\) and \(x=4\). The aixs of the symmetry is halfway between these at \(x=-1\).
If we multiply out the brackets the coefficient of \(x\)2 is 1. As this is \(a\textgreater0\) the parabola has a minimum turning point. The y coordinate when \(x=-1\) is -25 so the minimum turning point is (-1, -25).
Question
From the equation \(y = - {(x + 4)^2} - 5\), write down the co-ordinates and nature of the turning point and the equation of the axis of symmetry.
Since \(k = - 1\), then this parabola will have a maximum turning point at (-4, -5) and hence the equation of the axis of symmetry is \(x = - 4\).
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