Question

16. Determine a quadratic function `f ′ defined by f(x) = ax2 + bx + c if f(0)= 6, f(2) = 11 and f(- 3) = 6

Answer 1

Step-by-step explanation:

f(x)= ax^2+bx+c.

f(0)= a(0)^2+b(0)+c.

or, 6=0+0+c.

or, 6=c.

Now, f(2)=a(2)^2+b(2)+c.

or, 11=4a+2b+6.

or, 11-6=4a+2b.

or, 4a+2b=5.

or, 2(2a+b)=5.

or, 2a+b= 5/2..............(i).

Now,f(-3)=a(-3)^2+b(-3)+c.

or, 6=9a-3b+6.

or, 9a-3b=0.

or,3(3a-b)=0.

or, 3a-b=0...............(ii)

Now adding equation (i) and (ii):-

2a+b+3a-b=5/2+0.

or, 5a=5/2.

or, a= 5÷2×5.

or, a= 1/2.

Now, substitute this value in equation (ii):-

3a-b=0.

or, 3(1/2)-b=0.

or, 3/2-b=0.

or, 3/2=b.

Now, the quadratic function 'f' ax^2+bx+c= 1/2x^2+3/2x+6.

Now, divide it by 2:-

so, we get x^2+3x+3.

HOPE IT HELPS.........