Determine the Vertex and Axis of Symmetry for the parabola $y={(x+2)}^2$, and determine which direction the parabola will open.

• A. The parabola opens upwards; Vertex: $(-2,0)$; Axis of Symmetry: $x=-2$
• B. The parabola opens to the right; Vertex: $\(\left\)(-2,0\(\right\))$; Axis of Symmetry: $y=-2$
• C. The parabola opens upwards; Vertex: $(2,0)$; Axis of Symmetry: $y=-2$
• D. The parabola opens to the right; Vertex: $\(\left\)(-2,0\(\right\))$; Axis of Symmetry: $x=-2$

Answer: (A)

Verified step by step guidance

1. Identify the given equation of the parabola: \(y=\left(x+2\right)^2\). This is in the form \(y = (x - h)^2\), where \((h, k)\) is the vertex.
2. Rewrite the equation to match the vertex form \(y = (x - h)^2 + k\). Here, \(x + 2\) can be seen as \(x - (-2)\), so \(h = -2\) and \(k = 0\).
3. Determine the vertex from the values of \(h\) and \(k\). The vertex is at the point \((h, k)\), which is \((-2, 0)\) in this case.
4. Find the axis of symmetry, which is the vertical line that passes through the vertex. Since the vertex has \(x\)-coordinate \(-2\), the axis of symmetry is \(x = -2\).
5. Determine the direction the parabola opens by looking at the coefficient of the squared term. Since the coefficient of \((x+2)^2\) is positive (implicitly 1), the parabola opens upwards.