A turning point can be found by re-writting the equation into completed square form.

When the function has been re-written in the form `y = r(x + s)^2 + t`, the minimum value is achieved when `x = -s`, and the value of `y` will be equal to `t`.

The coordinate of the turning point is `(-s, t)`.

By completing the square, determine the coordinate of the turning point for the equation `y = 4x^2 + 4x - 4`.

Rewrite the equation `y = 4x^2 + 4x - 4` in completed square form:

`y = (2x + 1)^2 - 5`

The turning point is where `(2x + 1) = 0` or `x` = `-frac(1)(2)`

When `x=-frac(1)(2)`, `y = -5`.

Answer: (`-frac(1)(2)`,-5)

By completing the square, determine the `y` value for the turning point for the function `f(x) = x^2 + 4x + 7`

Complete the square:

`x^2 + 4x + 7 = (x+2)^2 + 3`

When `x` = -2, the bracket evaluates to zero, leaving a residual value of 3. This is the `y` value of the turning point.

Answer: `y=3`

See also Completing the Square

Check out our iOS app: tons of questions to help you practice for your GCSE maths. Download free on the App Store (in-app purchases required).