WMA11 Jan 2023

• WMA11/01 (Edexcel) IAL P1 January 2023, Q7(Graphs & Translation: Reciprocal Graphs & Transformations, Simulktaneous Equation: Intersections)

  • On Diagram 1, sketch a graph of the curve C with equation

y=6x       x≠0

(2)

The curve C is transformed onto the curve with equation

y =6x-2             x ≠ 2

• • Fully describe this transformation.

The curve with equation

y =6x-2         x ≠ 2

and the line with equation​​ 

y=kx+7​​ where k is a constant

intersect at exactly two points, P and Q.

Given that the x coordinate of point P is -4

• • find the value of k,

(2)

• • find, using algebra, the coordinates of point Q.

(Solutions relying entirely on calculator technology are not acceptable.)

(4)

SOLUTION

a-

b-​​ 

In case of this question,​​ 

fx=6x 

Have a look at the second point of the flash card. The constant added or subtracted inside the function represents the horizontal translation.​​ 

fx-2=6x-2

Translation in x-axis of 2 units to right or translation vector is given as 20.

c-​​ Since graphs of both equations intersect at point P and Q, point P cordinates must satisfyu both equations. So, substituting the value of x = - 4 in the reciprocal function.​​ 

y =6x-2

y=6-4-2=6-6 

y=-1

Thus, coordinates of P is​​ P-4, -1.

Now, substituting the coordinates of x and y in the equation of a straight line.​​ 

y=kx+7

y=kx+7

-1=k-4+7

-1=-4k+7

4k=8

k=2 

d-​​ Solving both equations simultaneously.

y=6x-2       (1)

y=2x+7      (2)

On equating both equations,​​ 

2x+7=6x-2

2x+7x-2=6

2x2-4x+7x-14=6

2x2+3x-20=0

2x-5x+4=0

2x-5=0        x+4=0

x=52       x=-4

Considering x= 5/2 as it is given in the question that -4 is the x-cordinate of point P.

You may substitute​​ x=52​​ in the equation of a straight line​​ y=2x+7​​ or equation of reciprocal function ​​ y =6x-2. I have selected staright line equation here.

y=252+7

y=12

Hence,

Q52, 12