Answer:
Hence, the quadratic equation is:
[tex]f(x)=-3x^2+x=-x(3x-1)[/tex]
Step-by-step explanation:
Let the quadratic formula be given by:
[tex]f(x)=ax^2+bx+c[/tex]
Now we are given the interpolating points and there corresponding values as:
(-1,-4), (0,0) and (2,-10).
this means then x=-1 f(x)=-4
when x=0 then f(x)=0
and when x=2 then f(x)=-10
so we first put x=0
then f(x)=0=c
hence c=0.
now we are left with the function:
[tex]f(x)=ax^2+bx------(1)[/tex]
Hence now we put x=-1 in equation (1)
we get:
[tex]f(x)=a-b=-4------(2)[/tex]
now we put x=2
[tex]f(x)=4a+2b=-10------(3)[/tex]
On solving equation (2) and (3) by elimination we get:
Multiply equation (2) by 2 and add to equation (3) we obtain;
2a-2b= -8
4a+2b= -10
---------------------------
6a=-18
⇒ a= -3 on dividing both side by 6.
Hence on putting the value of a in equation (2) we get:
b=1
Hence, the quadratic equation is:
[tex]f(x)=-3x^2+x=-x(3x-1)[/tex]
