for the equation: (x - 2)2 = - 4(y + 1); identify axis of symetryQuestion 1Select one:x = 2y = 2x = 1y = -1Clear my choice◄ weekend sheet t3 w8Jump to...

1. Break Down the Problem

The given equation is $(x - 2)^2 = -4(y + 1)$. This is a transformed parabola. To find the axis of symmetry, we need to rewrite the equation in a standard form that reveals its properties.

2. Relevant Concepts

The standard form for a parabola that opens vertically is given by $(x - h)^2 = 4p(y - k)$, where $(h, k)$ is the vertex of the parabola and the axis of symmetry is $x = h$.

3. Analysis and Detail

1. Rewrite the given equation: $(x - 2)^2 = -4(y + 1)$ This can be compared with the standard form: $(x - h)^2 = 4p(y - k)$ Here, we can identify:

   • $h = 2$
   • $k = -1$
   • $4p = -4$ which gives us $p = -1$

2. Since $h = 2$, the axis of symmetry is given by the equation: $x = h = 2$

4. Verify and Summarize

We have identified the vertex of the parabola at $(2, -1)$ and confirmed that the axis of symmetry is the line $x = h$.

Final Answer

The axis of symmetry for the equation $(x - 2)^2 = -4(y + 1)$ is $x = 2$.