Given three points (-1,1) (1,3) (-2,12) how do you write a quadratic function in standard form with the points?

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Answer 1 · 2016-05-14T12:46:32

#f(x) = 4x^2+x-2#

Suppose #f(x) = ax^2+bx+c#

The three points satisfy this equation, so we have:

#1 = f(-1) = a-b+c#

#3 = f(1) = a+b+c#

#12 = f(-2) = 4a-2b+c#

Hence:

#2b = (a+b+c)-(a-b-c) = 3 - 1 = 2#

So: #b=1#

Substituting this into the equations we have and rearranging a bit we get:

#a+c = 2#
#4a+c = 14#

Subtracting, we find:

#3a=12#

Hence #a=4# and #c=-2#

So #f(x) = 4x^2+x-2#