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y=-x^2+4x+3

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1 Answer

To answer this question you should use the quadratic formula.

-b±√(b^2-4ac)

         2

ax^2+bx+c

So a=-1 b=4 and c=3

Fill in the quadratic formula:

-4±√((-4)^2-4(-1)(3))

           2(-1)

Simplify:

-4±√(16+12)

       -2

-4±√(28)

    -2

You can pull a 4 out of 28 to make it:

-4±2√(7)

   -2

Simplify again:

2±√(7)*

*Note: you can divide by -2 and the plus or minus sign still "applies."

That gives us:

-x^2+4x+3 = (-x+(2+√(7))(x-(2-√(7))

Now, double check by FOILing the factored form:

(-x+(2+√(7))(x-(2-√(7)) = -x^2+(2-√(7))x+(2+√(7))x-(2+√(7))(2-√(7))

=-x^2+2x-√(7)x+2x+√(7)x-(4-2√(7)+2√(7)-7)

=-x^2+2x+2x+√(7)x-√(7)x-(4-7)
=-x^2+4x-(-3)

=-x^2+4x+3

So the answer is definitely: (-x+(2+√(7))(x-(2-√(7))

Comments

Nick's answer is complete, and correct. It would have been a much easier problem if that nasty (-) hadn't been there with the x2 term.

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