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2017 Maths AS/A Levels TECHNOLOGY First notice that for all values of b , the curve of y = x 2 + bx + 2 passes through the point with coordinates ( 0, 2 ) so as b changes, the curves are pivoted at this point. Explore this using graphing software. Seeing what happens raises other natural questions: • Does the minimum point trace out a parabola? • What if you change the coefficient of x 2 instead? • Are there similar questions to ask about a cubic? 2 By completing the square, y = x + b b2 , you can see that b affects both + 2 − 2 4 b 2 coordinates of the turning point: − , 2 − b2 . All such points lie on the parabola 4 y= 2 − x 2 . 1 of 1 AE 05/04/2016 Version 1.0