How do you solve quadratic equations with negative coefficients?

You can write -4x^2+4x-1=0 as 4x^2-4x+1=0

Take the negative away from the variable and apply it to the other numbers. You should get:
X^2+2x-3=0
Now you can factor.
The numbers are -1 and 3, because -1+3= 2 and -1x3=-3.
With that figured out, here are the factors:
(x-1)(x+3)=0
Now solve and you get
X=1 and -3 as the roots.

Therefore the intercepts are (1,0) and (-3,0)
---------------
-4x^2+4x-1
4x^2-4x+1
(2x-1)(2x-1)
Or (2x-1)^2
X=1/2

(1/2,0)

Dear Jake Garner,

-x^(2)-2x+3=0

Multiply each term in the equation by -1.
-x^(2)*-1-2x*-1+3*-1=0*-1

Multiply -x^(2) by -1 to get x^(2).
x^(2)-2x*-1+3*-1=0*-1

Multiply -2x by -1 to get 2x.
x^(2)+2x+3*-1=0*-1

Multiply 3 by -1 to get -3.
x^(2)+2x-3=0*-1

Multiply 0 by -1 to get 0.
x^(2)+2x-3=0

Use the quadratic formula to find the solutions.  In this case, the values are a=1, b=2, and c=-3.
x=(-b\~(b^(2)-4ac))/(2a) where ax^(2)+bx+c=0

Use the standard form of the equation to find a, b, and c for this quadratic.
a=1, b=2, and c=-3

Substitute in the values of a=1, b=2, and c=-3.
x=(-2\~((2)^(2)-4(1)(-3)))/(2(1))

Expand the exponent (2) to the expression.
x=(-2\~((2^(2))-4(1)(-3)))/(2(1))

Squaring a number is the same as multiplying the number by itself (2*2).
x=(-2\~((2*2)-4(1)(-3)))/(2(1))

Multiply 2 by 2 to get 4.
x=(-2\~((4)-4(1)(-3)))/(2(1))

Remove the parentheses around the expression 4.
x=(-2\~(4-4(1)(-3)))/(2(1))

Multiply 1 by -3 to get -3.
x=(-2\~(4-4(-3)))/(2(1))

Multiply -4 by the -3 inside the parentheses.
x=(-2\~(4-4*-3))/(2(1))

Multiply -4 by -3 to get 12.
x=(-2\~(4+12))/(2(1))

Add 12 to 4 to get 16.
x=(-2\~(16))/(2(1))

Pull all perfect square roots out from under the radical.  In this case, remove the 4 because it is a perfect square.
x=(-2\4)/(2(1))

Multiply 2 by the 1 inside the parentheses.
x=(-2\4)/(2)*1

Multiply 2 by 1 to get 2.
x=(-2\4)/(2)

First, solve the + portion of \.
x=(-2+4)/(2)

Add 4 to -2 to get 2.
x=(2)/(2)

Cancel the common factor of 2 the expression (2)/(2).
x=(<X>2<x>)/(<X>2<x>)

Remove the common factors that were cancelled out.
x=1

Next, solve the - portion of \.
x=(-2-4)/(2)

Subtract 4 from -2 to get -6.
x=(-6)/(2)

Move the minus sign from the numerator to the front of the expression.
x=-(6)/(2)

Cancel the common factor of 2 the expression -(6)/(2).
x=-(^(3)<X>6<x>)/(<X>2<x>)

Remove the common factors that were cancelled out.
x=-3

The final answer is the combination of both solutions.
x=1,-3

Thanks for the interesting question!
and  You're welcome

Nope!

 - (x + 3)*(x - 1) = 0

x + 3 = 0, x1 = - 3

x - 1 = 0, x2 = 1

( - 3, 0) = x1 - int

(1, 0) = x2 - int

  - 4x^2 + 4x - 1 = - (2*x - 1)^2

- (2*x - 1)^2 = 0

x1 = x2 = 1/2

(1/2, 0) = x1 - int

(1/2, 0) = x2 - int