Select the statement that is true for the equation y=−(x+2)2−6 (3 points) The parabola opens , has an axis of symmetry at x= , and a vertex at

Answer 1

Given the equation of the parabola \( y = -(x + 2)^2 - 6 \), we can analyze its properties step-by-step:

1. Opens: The equation has a negative sign in front of the square term \(-(x + 2)^2\), indicating that the parabola opens downward.

2. Axis of symmetry: The standard form of a parabola can be written as \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex. In the given equation, it's in the form \( y = -1(x + 2)^2 - 6\). Here, \( h = -2\) (since \( x + 2 = x - (-2) \)). Therefore, the axis of symmetry is the vertical line at \( x = -2 \).

3. Vertex: The vertex is given by the point \((h, k)\). From the equation, we have \( h = -2\) and \( k = -6\). Therefore, the vertex is at the point \((-2, -6)\).

Combining all information, we conclude:

• The parabola opens downward.
• It has an axis of symmetry at \( x = -2 \).
• The vertex is at the point \((-2, -6)\).

Thus, the completed statement is:

The parabola opens downward, has an axis of symmetry at \( x = -2 \), and a vertex at \((-2, -6)\).