Identify the quadratic function that contains the points (-1,-4), (0,0) and (2,-10).

Hence, the quadratic equation is:

Step-by-step explanation:

Let the quadratic formula be given by:

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:

Hence now we put x=-1 in equation (1)

we get:

now we put x=2

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

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       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: