GCSE(F), GCSE(H),

If the coefficient (the multiple) of the x2 term is positive, then the turning point is a minimum. If negative, the turning point is a maximum.

A quadratic curve is vertically symmetrical about its turning point, or vertex.

The x-value for the turning point is given by -frac(b)(2a). Substituting this value into the equation gives the y-value.

## Examples

1. What are the coordinates for the turning point for the equation y = x2 - 5x + 6?

The x-value is given by -frac(b)(2a) = -frac(-5)(2 xx 1) = 2.5. Substituting (2.5)2 - 5(2.5) + 6 = -0.25.
The x value is given by -frac(b)(2a) = -frac(6)(2x-3) = 1. Substitute for y = -3(1)2 + 6(1) + 6 = 9. Turning point is (1, 9)