SOLUTION: Find the vertex, focus, and the directrix of the parabola 𝑦2 − 4𝑦 + 4𝑥 + 4 = 0 Unsure I solved the equation. 𝑦2 − 4𝑦 + 4𝑥 + 4 = 0 𝑦2 − 4𝑦 + 4𝑥 +

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the vertex, focus, and the directrix of the parabola 𝑦2 − 4𝑦 + 4𝑥 + 4 = 0 Unsure I solved the equation. 𝑦2 − 4𝑦 + 4𝑥 + 4 = 0 𝑦2 − 4𝑦 + 4𝑥 +      Log On


   

Question 1202858: Find the vertex, focus, and the directrix of the parabola 𝑦2 − 4𝑦 + 4𝑥 + 4 = 0
Unsure I solved the equation.
𝑦2 − 4𝑦 + 4𝑥 + 4 = 0
𝑦2 − 4𝑦 + 4𝑥 + 4−4𝑥 − 4 = 0 −4𝑥 − 4
− 𝑦2 − 4𝑦 =−4𝑥 - 4
− 𝑦2 − 4𝑦 + 4 =−4𝑥 − 4 + 4
(y−2)² = −4x
(y−2)² = 4(−1)(x−0)
Horizontal Parabola (opens left)
(y−k)² = 4p(x−h)
Vertex (0, 2)
Focus (−1, 2)
Directrix = 1
p = −1
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!

y%5E2-4y%2B4%2B4x=0
%28y-2%29%5E2%2B4x=0
4x=-%28y-2%29%5E2
compare to 4px=-%28y-2%29%5E2
p=1, distance of vertex to directrix
Vertex (0, 2)
Directrix at x=1.
Focus at (-1, 2)

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

You have the correct answers. Nice work.
I have confirmed the answers with GeoGebra.

The only error that I see is the -y%5E2-4y portion should instead be y%5E2-4y.