MATHEMATICS IB 2020

Question

f(x) Let = 3x2−6x+p . The equation f(x) = 0 

has two equal roots. 

18a.Write down the value of the discriminant. 

18b. Hence, show that . p = 3 

18c.The graph of F has its vertex on the x -axis. Find the coordinates of the vertex of the graph of f 

18d. The graph of F has its vertex on the x -axis. Write down the solution of f(x) = 0 

f 18e.The graph of F has its vertex on the x -axis. The function can be written in the form f(x) = a(x − h)2 + k . Write down the value of a 

. 

f 18f.The graph of F has its vertex on the x -axis. The function can be written in the form f(x) = a(x − h)2 + k . Write down the value of h 

Answer 1

Parts a-b:

Then the discriminant must be zero

A=3 vB = -6 C=p

0 = B^2 - 4ac = 36 - 4(3)(p) = 36 - 12p

p=3

Parts C-f:

b/(2a) = 6/6 = 1

3(1)^2 + -6(1) + 3 = 3-6+3 =0

the vertex is (1,0)=(h,k)

y = C(x-1)^2

per the original function f(0) = 3, so

3 = C(0-1)^2

3 = C(-1)^2

3=C(1)

C = 3

So the function is y = f(x) = 3(x-1)^2

Note that 3x^2 - 6x + 3 = 3(x^2 - 2x + 1) = 3(x-1)^2