Question

Find f(6) if it is given that f(0)=-3, f(1)=6, f(2)=8, f(3)=12

Answer 1

Answer:

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Answer 2

Answer: f(0)=-3, f(1)=6, f(2)=8, f(3)=12, f(6) = 162

Step-by-step explanation:

∵ $f(x)=ax^{2} +bx+c$

Given - f(0) = -3

             f(1) = 6

             f(2) = 8

             f(3) = 12

Find       f(6) = ?

f(0) = f(x)     (x=0)

f(0) = $a(0^{2} )+ b(0)+c =-3$

f(0) = c = -3 …(1)

Similarly , $f(1)= a(1^{2} ) +b(1) + c = 6$

                f(1) = a + b + c = 6 ….(2)

                f(2) = 4a + 2b + c = 8.....(3)

                f(3) = 9a + 3b + c = 12.....(4)

putting the value of c = -3 in eq.(2)

  a + b -3 = 6

 a + b = 9...(5)      a = 9-b

in eq.(3) putting the values

4a + 2b + c = 8

4(9-b) + 2b + (-3) = 8

36 - 4b + 2b = 11

36 - 2b = 11

36 - 11 = 2b

25 = 2b

b = $\frac{25}{2}$ = 12.5

Now put the values of b and c in eq.(4)

9a + 3b + c = 12

9a + 3 x 25/2 = 12+3

9a + 75/2 = 15

9a = 15 - 75/2

9a = -45/2

a = $\frac{-45}{18}$

a = -2.5

Now put the values of a, b, c in f(6)

$f(6)=a(6)^{2} +b(6)+c$

f(6) = -2.5x36 + 12.5x6 + (-3)

      = 90 + 75 - 3

       = 165 - 3

f(6)   = 162.....answer