Working out the coordinates of the turning point of a quadratic equation is a 3-step process.
(Assume our quadratic equation has 2 roots)
- Find the roots of the quadractic equation (done by solving for the variable ‘x’)
- Work out the middle point between these 2 roots
- 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