Find the Vertex Form y^2-4y+4x+4=0

Problem

y2−4*y+4*x+4=0

Solution

1. Isolate the quadratic terms by moving the terms involving x and the constant to the right side of the equation.

y2−4*y=−4*x−4

2. Complete the square for the y terms by adding ((−4)/2)2=4 to both sides of the equation.

y2−4*y+4=−4*x−4+4

3. Factor the left side as a perfect square trinomial and simplify the right side.

(y−2)2=−4*x

4. Solve for x to put the equation into the standard vertex form for a parabola opening horizontally, which is x=a*(y−k)2+h

−4*x=(y−2)2

5. Divide both sides by −4 to isolate x

x=−1/4*(y−2)2

Final Answer

y2−4*y+4*x+4=0⇒x=−1/4*(y−2)2

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