Answer:
The parabola opens to the right
Step-by-step explanation:
The given equation corresponds to a parabola.
[tex]y^{2} -4x + 4y - 4 = 0[/tex]
We can rewrite this formula in vertex form ([tex]x = a(y - y_{0})^{2} + x_{0}[/tex]) to be able to locate the vertex and its direction
[tex]-4x = -y^{2} - 4y + 4[/tex] (isolate 4x on the left)
[tex]x = \frac{y^{2}} {4} + y - 1[/tex] (divide both sides by -4)
[tex]x = \frac{1} {4} (y^{2} + 4y) - 1[/tex] (common factor [tex]\frac{1} {4}[/tex] between [tex]\frac{y^{2}} {4}[/tex] and [tex]y[/tex])
[tex]x = \frac{1} {4}(y^{2} + 4y + 4 - 4) - 1[/tex] (add and substract 4 to complete square)
[tex]x = \frac{1} {4}(y^{2} + 4y + 4) - 4 - 1[/tex] (associate to get square inside parentheses)
[tex]x = \frac{1} {4}(y + 2)^{2} - 5[/tex] (collapse square inside parentheses)
We can conclude the following:
- Its vertex is (-5, -2)
- Its axis of symmetry is y = -2
- Coefficient a = 1/4 is positive
The parabola opens to the right (see the attachment)
