Use the image to answer the question. Identify the vertex and axis of symmetry of the parabola.

Question

One point is (-1,16) another point is (-5,0) another point is (3,0)

Answer 1

To find the vertex and axis of symmetry of the parabola given the points (-1, 16), (-5, 0), and (3, 0), we can follow these steps:

1. Identify the Roots: The points (-5, 0) and (3, 0) are the roots (x-intercepts) of the parabola.

2. Find the Axis of Symmetry: The axis of symmetry of a parabola that opens either upward or downward is the vertical line that divides it into two mirror images. It can be found by taking the average of the x-coordinates of the roots:

   \[ x = \frac{x_1 + x_2}{2} = \frac{-5 + 3}{2} = \frac{-2}{2} = -1 \]

   So, the axis of symmetry is \( x = -1 \).

3. Find the Vertex: The vertex lies on the axis of symmetry. To find the y-coordinate of the vertex, substitute \( x = -1 \) into the equation of the parabola. However, since we can see that the y-coordinate of the point (-1, 16) is provided, we can directly say that the vertex is:

   \[ (-1, 16) \]

Summary:

• Vertex: (-1, 16)
• Axis of Symmetry: \( x = -1 \)