SOLUTION: I've been instructed to find the general equation given this information: zeros at (-1-sqrt(3)) and (-1+sqrt(3)). A point intersected by the parabola of this equation is (1,2). I h

Question 204125: I've been instructed to find the general equation given this information: zeros at (-1-sqrt(3)) and (-1+sqrt(3)). A point intersected by the parabola of this equation is (1,2). I have determined that a=-(2/3).
I now have the equation -(2/3)*(x-1-sqrt(3))*(x-1+sqrt(3)). I'm supposed to find the general equation, "fully expanded, in descending order of powers". I've tried simplifying this equation - i.e. factoring - but cannot find a 'simpler' equation that goes through the point (1,2). I did graph the equation I'm trying to simplify, and it does indeed go through (1,2). So, my question is, can this equation be simplified further, or do I have my answer? If this can be simplified further, would you please show me how? Thank you very much! Julia.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
f(x) = -(2/3)*(x-1-sqrt(3))*(x-1+sqrt(3))
---
f(x) = (-2/3)
----
Notice that that factors are now in the form (a-b)(a+b)
which multiplies to be a^2-b^2.
----
f(x) = (-2/3)
---
f(x) = (-2/3)
---
f(x) = (-2/3)(x^2-2x-2)
===============================
Cheers,
Stan H.
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