There are 3 possible ways of working out the coordinates of the vertex of a quadratic equation on a graph. These are:

1) Using the Axis of Symmetry formula of the parabola

2) Using the roots of the quadratic equation (where the parabola intersects the x-axis)

3) Using completing the square (where the parabola does not interect the x-axis)

1. Using the Axis of Symmetry (AoS) of the Parabola

2. Using the Roots of the Quadratic Equation

EXAMPLE I – Using graphs to find the coordinates

EXAMPLE II – Using the quadratic formula to find the coordinates

3. Using Completing the Square

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Quadratic Curve - Coordinates of the Turning Point (Part II)
Direct & Inverse Proportions