Sketch the curve with equation
y=x2(2x−a)y = x^2(2x - a)y=x2(2x−a)
where a>0a > 0a>0.
The polynomial p(x)p(x)p(x) is given by
p(x)=x2(2x−a)−64p(x) = x^2(2x - a) - 64p(x)=x2(2x−a)−64
It is given that x−8x - 8x−8 is a factor of p(x)p(x)p(x). Use the factor theorem to show that a=15a = 15a=15.
State the transformation which maps the curve with equation y=x2(2x−15)y = x^2(2x - 15)y=x2(2x−15) onto the curve with equation y=x2(2x−15)−64y = x^2(2x - 15) - 64y=x2(2x−15)−64.
The polynomial x2(2x−15)−64x^2(2x - 15) - 64x2(2x−15)−64 can be written as (x−8)(2x2+bx+c)(x - 8)(2x^2 + bx + c)(x−8)(2x2+bx+c). Without finding the values of bbb and ccc, use your knowledge of the transformation in part (b)(ii) and the sketch in part (a) to explain why
b2<8cb^2 < 8cb2<8c
Practise Edexcel A Level Maths 2.6 Combining Transformations with exam-style questions for A Level Maths. 17 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.