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Quadratic Curve – Coordinates of the Turning Point (Part I)

Working out the coordinates of the turning point of a quadratic equation is a 3-step process.

(Assume our quadratic equation has 2 roots)

  1. Find the roots of the quadractic equation (done by solving for the variable ‘x’)
  2. Work out the middle point between these 2 roots
  3. Replace the value from step 2 into the quadratic equation and find ‘y’

The values from step 2 and step 3 are the respective ‘x’ and ‘y’ coordinates of the turning point.

EXAMPLE I – Using graphs to find the coordinates

EXAMPLE II – Using the quadratic formula to find the coordinates

Suppose we have the following equation:

We can’t use factoring to find the roots; so we use the quadratic formula.

Now for STEP 2 and STEP 3