GCSE(F), GCSE(H),

If the coefficient (the multiple) of the *x*^{2} 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.

1. What are the coordinates for the turning point for the equation *y* = *x*^{2} - 5*x* + 6?

Answer: (2.5, -0.25)

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.

2. What are the coordinates for the turning point for *y* = -3*x*^{2} + 6*x* + 6?

Answer: (1, 9)

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)

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