Question

Match each equation with the correct feature.(4 points)
y=(x+4)2−1

Answer 1

To match the equation \( y = (x + 4)^2 - 1 \) with its features, we can analyze its components to identify key characteristics:

1. **Vertex**: The vertex form of a quadratic equation is given by \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex. In this case, the equation can be rewritten to identify the vertex. The vertex is \((-4, -1)\).

2. **Axis of Symmetry**: The axis of symmetry can be found using the x-coordinate of the vertex. The equation of the axis of symmetry is \( x = -4 \).

3. **Direction of Opening**: Since the coefficient of the squared term is positive (1 in this case), the parabola opens upwards.

4. **Y-intercept**: To find the y-intercept, set \(x = 0\):
\[
y = (0 + 4)^2 - 1 = 16 - 1 = 15.
\]
So, the y-intercept is \( (0, 15) \).

With these features in mind, we can summarize:

- **Vertex**: \((-4, -1)\)
- **Axis of symmetry**: \( x = -4 \)
- **Direction of opening**: Upwards
- **Y-intercept**: \( (0, 15) \)

You can now match those features accordingly to the options given for your question.