graph of function mx^2nx+p passes through (-1,0),(0,3),(3,0). what is m,n,p?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should substitute the coordinates of each point, one by one, in equation of the function such that:

`m*(-1)^2 + n*(-1) + p = 0`

`p = 3`

`m*(3)^2 + n*3 + p = 0`

You should solve for m,n and p the system of simultaneous equations such that:

`m - n + p = 0`

`p = 3`

`9m + 3n + p = 0`

Substituting 3 for p in the first and the third equations yields:

`m - n = -3`

`9m + 3n = -3`

You need to multiply by 3 the first equation such that:

`3m -3n = -9`

`9m + 3n = -3`

You need to add the equations such that:

`12m = -12 =gt m = -1`

You need to substitute -1 for m in equation `m - n = -3`  such that:

`-1 - n = -3 =gt -n = -3 + 1 =gt n = 2`

Hence, evaluating the coefficients m,n,p yields `m=-1,n=2`  and `p=3` .

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