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 .
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AE 05/04/2016
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