WMA11 October 2022

6. WMA11/01 Edexcel IAL P1 October 2022, Q6 (Graphs &​​ Transformation: Sketching Cubic & Reciprocal Graphs)

(a) Given that k is a positive constant such that 0 < k < 4 sketch, on separate axes, the graphs of​​ 

(I)​​ y = 2x – kx + 42

(ii)​​ y =kx2

showing the coordinates of any points where the graphs cross or meet the coordinate axes,​​ leaving coordinates in terms of k, where appropriate.​​ 

(5)

(b) State, with a reason, the number of roots of the equation​​ 

2x – kx + 42 =kx2

(1)

SOLUTION

a-​​ 

i-​​ y = 2x – kx + 42

For y-intercept, put x=0

y = 2x – kx + 42

y = 2×0 – k0 + 42

y=-k42

y= -16k

0,-16k

For x-intercept, put y=0

y = 2x – kx + 42

0=2x-kx+42

2x-k=0              x+42=0

  x=k2                x=-4 

ii-​​ y =kx2

b-​​ 

There is only one root of the equation​​ as it only graph of​​ 2x – kx +42​​ &​​ kx2​​ intersects once in the first quadrant.​​ 

For better understanding have a look on the sketch below.​​