Turning Points for Quadratics

Turning Points for Quadratics

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?

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.

graph showing 2 x squared - 5  x - 6

2. What are the coordinates for the turning point for y = -3x2 + 6x + 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)