WMA11 June 2021

8. WMA11/01 Edexcel​​ IAL P1 June 2021 Q8​​ (Quadratics: Completing the Square & Graphs and Transformations: Cubic Graphs)

The curve C1​​ has equation​​ 

y = 3x2 + 6x + 9 

(a) Write​​ 3x2 + 6x + 9 in the form​​ 

ax + b2 + c 

where a, b and c are constants​​ to be found.​​ 

(3)

The point P is the minimum point of C1​​ 

(b) Deduce the coordinates of P.​​ 

(1)

A different curve C2​​ has equation

y = Ax3 + Bx2 + C x + D 

where A, B, C and D are constants.​​ 

Given that C2​​ 

• passes through P​​ 

• intersects the x-axis at –4, –2 and 3​​ 

(c) find, making​​ your method clear, the values of A, B, C and D.​​ 

(5)

SOLUTION​​ 

a-​​ 

3x2+6x+9

=3x2+2x+9

=3x+12-1+9

=3x+12-3+9

=3x+12+6

b-​​ 

The quadratic equation can be expressed in the form of completing square form as​​ y=ax-p2+q, where (-p ,q) is the vertex of the quardratic function.

So, in case of this question, the​​ equation is​​ 

y=3 x+12+6

P-1,6

c- The curve intersects x-axis or the solutions of curve are

x= -4           x=-2             x=3

x+4=0              x+2=0            x-3=0 

So the equation of a curve would be​​ 

y=Ax+4x+2x-3

It is also given that the curve C2​​ passes through the point (-1, 6), so it must satisfy the equation.​​ 

6=A-1+4-1+2-1-3

6=A31-4

6=12A

 A=-12

So, the equation of the curve​​ after putting the value of A is

y=-12x+4x+2x-3

y= -12x+4x2-x-6

y=-12x3-x2-6x+4x2- 4x-24

y=12x3+3x2-10x-24

y=-12x3-32x2+5x+12

On comparing the above expression with​​ y = Ax3 + Bx2 + C x + D, we get the value of A, B, C, & D as​​ 

A=-12, B=-32, C=5,& D=12

Thus,

A=-1/2,

B=-3/2,

C=5, &

D=12